Hyperbolic and inverse functions · Short practice

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Recall

Hyperbolic and inverse-function derivatives — objective 1

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=13 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(11 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find f′(0).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Hyperbolic and inverse-function derivatives — objective 1

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=14 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(12 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find f′(0).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Hyperbolic and inverse-function derivatives — objective 2

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=14 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(12 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find f″(0).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Hyperbolic and inverse-function derivatives — objective 2

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=15 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(13 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find f″(0).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Hyperbolic and inverse-function derivatives — objective 3

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=15 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(13 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find f‴(0).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Hyperbolic and inverse-function derivatives — objective 3

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=16 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(14 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find f‴(0).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Hyperbolic and inverse-function derivatives — objective 4

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=16 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(14 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find \(\displaystyle f^{(4)}(0)\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Hyperbolic and inverse-function derivatives — objective 4

Maths4U Original · Short practice

Near \(\displaystyle x=0\), let \(f(x)=17 \log{\left(x + 2 \right)} + \operatorname{asinh}{\left(15 x \right)}\). All derivatives below are evaluated at \(\displaystyle x=0\).

Find \(\displaystyle f^{(4)}(0)\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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