Best solutions to - "Find the derivatives of the function defined as..."

Jason Yuhas

Answered question

2021-12-06

Find the derivatives of the function defined as follow

y = \cos^{5} x

Neunassauk8

Beginner2021-12-07Added 30 answers

Step 1: Use the power rule and the chain rule of differentiation-
To find the derivative of the function,

y = \cos^{5} x

, use the power rule,

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

and the chain rule of differentiation,

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

. Apply the power rule to

\cos^{5} x

and chain rule to

\cos x

y = \cos^{5} x

\frac{d y}{d x} = \frac{d}{d x} (\cos^{5} x)

= 5 \cos^{4} x \frac{d}{d x} (\cos x)

= 5 \cos^{4} x (- \sin x)

= - 5 \sin x \cos^{4} x

Step 2: Simplify the resulting expression-
Simplify the resulting expression and obtain the answer,

- 5 \sin x \cos^{4} x

5 \cos^{4} x (- \sin x) = - 5 \sin x \cos^{4} x

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