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tbbfiladelfia6l

Answered question

2021-12-04

Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

y = \csc (t^{2} + t)

Answer & Explanation

Jeffrey Parrish

Beginner2021-12-05Added 15 answers

Step 1
The given function is

y = \csc (t^{2} + t)

.
The chain rule is given by

\frac{d}{d x} [f (g (x))] = f^{'} (g (x)) \cdot g^{'} (x)

.
Step 2
The derivative is obtained as follows.

\frac{d y}{d x} = \frac{d}{d x} [\csc (t^{2} + t)]

= - \csc (t^{2} + t) \cot (t^{2} + t) \frac{d}{d t} (t^{2} + t) (∵ \frac{d}{d x} (x^{n}) = n x^{n - 1})

= - \csc (t^{2} + t) \cot (t^{2} + t) (2 t + 1)

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