Basic differentiation

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Vicky Hall

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Vicky Hall 8 years, 11 months ago

Created this as a copy of Vicky's copy of Differentiation 1 - Basic Polynomial Expressions.

Name	Status	Author	Last Modified
Differentiation 1 - Basic Polynomial Expressions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 2 - Basic Polynomial Expressions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 3 - Basic Polynomial Expressions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 4 - Trigonometric Functions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 5 - Trigonometric Functions	Ready to use	Katie Lester	23/03/2021 15:11
Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	Ready to use	Katie Lester	01/06/2016 09:47
Jinhua's copy of Differentiation 5 - Trigonometric Functions	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 3 - Basic Polynomial Expressions	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 2 - Basic Polynomial Expressions	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 4 - Trigonometric Functions	Ready to use	Jinhua Mathias	27/08/2024 16:37
CF Maths Portfolio - Basic Polynomial Expressions 2	Has some problems	Jinhua Mathias	28/08/2024 12:15
CF Maths Portfolio - Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	Ready to use	Jinhua Mathias	27/08/2024 16:37
CF Maths In class test two mock paper question 1	Ready to use	Jinhua Mathias	28/08/2024 12:15
CF Maths In class test two mock paper question 5 (ii)	Ready to use	Jinhua Mathias	28/08/2024 12:15
CF Maths Portfolio 6 - Differentiation of Trigonometric Functions	Ready to use	Jinhua Mathias	28/08/2024 12:15
Bill's copy of CF Maths Portfolio 6 - Differentitation of Trigonometric Functions	Ready to use	Bill Foster	14/09/2016 13:31
Differentiation 1 - Basic Polynomial Expressions	Ready to use	Jinhua Mathias	28/08/2024 12:15
Vicky's copy of Differentiation 1 - Basic Polynomial Expressions	draft	Vicky Hall	01/07/2016 20:46
Basic differentiation	draft	Vicky Hall	25/07/2016 15:52
Jinhua's copy of Differentiation 4 - Trigonometric Functions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 5 - Trigonometric Functions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 2 - Basic Polynomial Expressions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 2 - Basic Polynomial Expressions	draft	Jinhua Mathias	28/08/2024 12:15
CF Maths Portfolio - Differentiation 2 - Basic Polynomial Expressions (with fractional coefficients)	Ready to use	Jinhua Mathias	27/08/2024 16:37
TRES SEIS Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:32
CUATRO CUATRO Derivada FT	draft	Marlon Arcila	08/09/2021 00:36
CUATRO TRES Derivada FT	draft	Marlon Arcila	08/09/2021 00:34
TRES DOS Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:27
TRES TRES Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:28
TRES CUATRO Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:29
TRES CINCO Derivadas R potencia y suma/resta	draft	Marlon Arcila	30/11/2021 00:55
CUATRO UNO Derivada FT	draft	Marlon Arcila	08/09/2021 00:33
CUATRO DOS Derivada FT	draft	Marlon Arcila	08/09/2021 00:35
Differentiation of Basic Polynomial Expressions (with second derivatives)	draft	Nigel Atkins	02/03/2017 10:49
cormac's copy of Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	cormac breen	17/04/2020 19:41
cormac's copy of cormac's copy of Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	cormac breen	06/03/2017 14:11
Pascal's copy of Differentiation of Basic Polynomial Expressions (with second derivatives)	draft	Pascal Philipp	07/08/2017 19:25
Ida's copy of TRES CINCO Derivadas R potencia y suma/resta	draft	Ida Landgärds	16/04/2018 12:23
Harry's copy of Differentiation of Basic Polynomial Expressions (with second derivatives)	draft	Harry Flynn	08/05/2018 12:22
Harry's copy of CF Maths Portfolio - Differentiation 2 - Basic Polynomial Expressions (with fractional coefficients)	draft	Harry Flynn	08/05/2018 16:53
Alison's copy of Vicky's copy of Differentiation 1 - Basic Polynomial Expression	draft	Alison Loddick	16/01/2019 15:40
Differentiation 1 - Basic Polynomial Expressions	draft	Xiaodan Leng	11/07/2019 06:54
Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	Xiaodan Leng	11/07/2019 06:55
Differentiation 4 - Trigonometric Functions	draft	Xiaodan Leng	11/07/2019 07:00
Differentiation 5 - Trigonometric Functions	draft	Xiaodan Leng	11/07/2019 07:01
Differentiation - Trigonometric Functions	draft	Kevin Bohan	27/01/2020 14:48
Musa's copy of 3 Differentiation - Trigonometric Functions	draft	Musa Mammadov	27/06/2023 01:34
Differentiation - Trigonometric Functions	Ready to use	Wan Mekwi	26/10/2020 11:35
Chain Rule 3 (H)	Ready to use	Chris Knapp	06/03/2025 11:19
Chain Rule 5 (M)	Ready to use	Chris Knapp	06/03/2025 11:20
Chain Rule 4 (M)	Ready to use	Chris Knapp	06/03/2025 11:20

There are 117 other versions that do you not have access to.

Question statement

Differentiate the following functions.

Give any introductory information the student needs.

			Name	Type	Generated Value

g	integer	5
bc	list	[ -3, -1, -4, 4 ]
cc	list	[ -5, -5, 5, -5 ]
dc	list	[ -12, 12, -13, -15 ]
ec	list	[ 25, -24, 27, 21 ]
fc	list	[ 19, 27, 26, 20 ]
ap	integer	5
bp	integer	4
cp	integer	3
dp	integer	2
h	integer	5
k	integer	8
l	integer	10

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$y=\simplify[basic,zeroterm,zerofactor,unitfactor]{{dc[2]}x^{dp}+{ec[2]}x+{fc[2]}}$

$\displaystyle \frac{dy}{dx}=$ Unnamed gap

Advice

Parts A and B

If $y=ax^n$ ,

$\frac{dy}{dx}=anx^{n-1}$ for all rational $n$ .

All we have to do to terms where $x$ is to a power of anything is times the coefficient of $x$ by the original power, and then take one away from the original power.

Don't be confused if there is no coefficient. The fact the term is there means the coefficient must be $1$ , but we don't tend to write it out as, for example $1x$ , we just say $x$ .

Part C

Remember that $\ln(x)$ differentiates to $\displaystyle \frac {1}{x}$ . It follows that $a \ln(x)$ differentiates to $\displaystyle \frac {a}{x}$ . If the $x$ term is actually, for example, $x+4$ or $2x-1$ , then we also need to use the chain rule and multiply our answer by the derivative of the $x$ term.

Let's differentiate $3 \ln(2x-1)$ as an example. Using the fact that $a \ln(x)$ differentiates to $\displaystyle \frac {a}{x}$ , we know that the first part of our answer will be

$\displaystyle \frac {3}{2x-1}$

We then need to find the derivative of $2x-1$ and then multiply the first part of our answer by this. The derivative of $2x-1$ is $2$ so the final answer will be

$\displaystyle \frac {3*2}{2x-1}$ = $\displaystyle \frac {6}{2x-1}$

Part D

Remember that $\cos(x)$ differentiates to $-\sin(x)$ . It follows that $a \cos(x)$ differentiates to $-a \sin(x)$ . Like in the previous example, if the $x$ term is actually something slightly more complicated then we also need to use the chain rule and multiply our answer by the derivative of the $x$ term.

Let's differentiate $4 \cos(3x+1)$ as an example. Using the fact that $a \cos(x)$ differentiates to $-a \sin(x)$ , we know that the first part of our answer will be

$\displaystyle -4 \sin(3x+1)$

We then need to find the derivative of $3x+1$ and then multiply the first part of our answer by this. The derivative of $3x+1$ is $3$ so the final answer will be

$\displaystyle -4*3 \sin(3x+1)$ = $\displaystyle -12 \sin(3x+1)$

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This question is used in the following exam:

Differentiation by Vicky Hall in Pretoria GEF Support Material.

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Vicky Hall 8 years, 11 months ago

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Basic differentiation

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Taxonomy: mathcentre

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Contributors

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Vicky Hall 8 years, 11 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`