Chain rule - hyperbolic and log functions - Numbas at mathcentre.ac.uk

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Chain rule - hyperbolic and log functions	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Differentiation: Chain Rule - Hyp Log	draft	Clare Lundon	14/08/2018 12:13

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Question statement

Write down the derivatives of the following functions $f(x)$ .

Note that in order to input the square of a function such as $\sinh(x)$ you have to input it as $(\sinh(x))^2$ , similarly for the other hyperbolic functions.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	4
b	integer	4
n	integer	6
a1	integer	-6
a2	integer	3
b1	integer	1
b2	integer	9

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Generated value: `integer`

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"Part b)" - prompt
"Part b)" → "Unnamed gap" - Correct answer

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1. Gap Mathematical expression
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Part b) Gap-fill
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Part c) Gap-fill
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$f(x)=\simplify[std]{ x ^ {n} * sinh({a1} * x + {b1})}$

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

Advice

Here is a table of the derivatives of some of the hyperbolic functions:

$f(x)$	$\displaystyle{\frac{df}{dx}}$
$\sinh(bx)$	$b\cosh(bx)$
$\cosh(bx)$	$b\sinh(bx)$
$\tanh(bx)$	$\simplify{b*sech(bx)^2}$

$f(x)=\simplify[std]{ x ^ {n} * sinh({a1} * x + {b1})}$

Use the product rule to obtain:

$\frac{df}{dx} = \simplify[std]{{n} * (x ^ {(n -1)}) * sinh({a1} * x + {b1}) + {a1} * (x ^ {n}) * Cosh({a1} * x + {b1})}$

$f(x)=\tanh(\simplify[std]{{a}x+{b}})$

Using the table above we get:

$\frac{df}{dx} = \simplify[std]{{a}*sech({a}x+{b})^2}$

$f(x)=\ln(\cosh(\simplify[std]{{a2}x+{b2}}))$

Using the chain rule we find:

$\frac{df}{dx} = \simplify[std]{{a2} * tanh({a2} * x + {b2})}$

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Chain rule - hyperbolic and log functions

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Generated value: `integer`

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Chain rule - hyperbolic and log functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`