Explained: "Use the Chain Rule to find the derivative...."

coexpennan

Answered question

2021-09-26

Use the Chain Rule to find the derivative.

y = \sin (x^{2})

timbalemX

Skilled2021-09-27Added 108 answers

Step 1
We have to find the derivative of given function by using chain rule:

y = \sin (x^{2})

We know the formula of derivatives,

\frac{d f (g (x))}{d x} = f^{'} (g (x)) \times \frac{d g (x)}{d x}

(chain rule)

\frac{{d x}^{n}}{d x} = n x^{n - 1}

\frac{d \sin x}{d x} = \cos x

Step 2
So finding derivative of given function with respect to 'x', we get

\frac{d y}{d x} = \frac{d \sin (x^{2})}{d x}

= \cos (x^{2}) \times \frac{{d x}^{2}}{d x}

= \cos (x^{2}) (2 x^{2 - 1})

= 2 x \cos (x^{2})

Hence, derivative of given function is

2 x \cos (x^{2})

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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