Harry's copy of Differentiation: Product rule

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Harry Flynn

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Harry Flynn 6 years, 11 months ago

Created this as a copy of Differentiation: Product rule.

Name	Status	Author	Last Modified
Differentiation: Product rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
CINCO CINCO Derivada producto	draft	Marlon Arcila	08/09/2021 00:39
Harry's copy of Differentiation: Product rule	draft	Harry Flynn	08/05/2018 12:46
Differentiation: Product rule	Ready to use	Simon Vaughan	20/08/2020 13:01

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Question statement

Differentiate the following function $f(x)$ using the product rule.

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			Name	Type	Generated Value

a	integer	7
s1	integer	-1
b	integer	-7
m	integer	8

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Generated value: `integer`

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$\simplify[std]{f(x) = x ^ {m} * cos({a} * x+{b})}$

$\displaystyle \frac{df}{dx}=\;$ Unnamed gap

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Advice

The product rule says that if $u$ and $v$ are functions of $x$ then

$\simplify[std]{Diff(u * v,x,1) = u * Diff(v,x,1) + v * Diff(u,x,1)}$

For this example:

$\simplify[std]{u = x ^ {m}}\Rightarrow \simplify[std]{Diff(u,x,1) = {m}x ^ {m -1}}$

$\simplify[std]{v = cos({a} * x+{b})} \Rightarrow \simplify[std]{Diff(v,x,1) = -{a} * sin({a} * x+{b})}$

Hence on substituting into the product rule above we get:

$\simplify[std]{Diff(f,x,1) = {m}x ^ {m-1} * cos({a} * x+{b})-{a}x^{m} * sin({a} * x+{b})}$

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Harry's copy of Differentiation: Product rule

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Taxonomy: mathcentre

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Checkpoint description

Harry Flynn 6 years, 11 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Harry's copy of Differentiation: Product rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 6 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`