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vestirme4

Answered question

2020-11-11

Calculating derivatives Find the derivative of the following functions.

y = \cos^{2} x

Neelam Wainwright

Skilled2020-11-12Added 102 answers

Step 1
We have to find derivatives:

y = \cos^{2} x

We know the derivatives formula,

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

\frac{d {(f (x))}^{2}}{d x} = 2 {(f (x))}^{2 - 1} \frac{d f (x)}{d x}

= 2 f (x) f^{'} (x)

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

Here

f (x) = \cos x

Step 2
Differentiating given function with respect to 'x', we get

y = \cos^{2} x

\frac{d y}{d x} = \frac{d \cos^{2} x}{d x}

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

= 2 \cos x (- \sin x)

= - 2 \sin x \cos x

= - 2 \sin 2 x

Hence, derivatives of given function is

- \sin 2 x

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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