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

melodykap

Answered question

2021-10-11

Find the derivatives of the functions defined as.

y = \cos^{4} x

Answer & Explanation

Laith Petty

Skilled2021-10-12Added 103 answers

Step 1
Given function,

y = \cos^{4} x

Step 2
Using the chain rule of the derivative,

\frac{d y}{d x} = \frac{d y}{d u} \frac{d u}{d x}

Let

u = \cos x \Rightarrow y = u^{4}

Now the derivative of y with respect to x,

\frac{d y}{d x} = \frac{d y}{d u} \frac{d u}{d x}

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

\frac{d y}{d x} = 4 u^{3} (- \sin x)

\frac{d y}{d x} = - 4 u^{3} \sin x

\frac{d y}{d x} = - 4 \cos^{3} x \sin x

Step 3
Final answer:

\frac{d y}{d x} = - 4 \cos^{3} x \sin x

Jeffrey Jordon

Expert2022-11-15Added 2605 answers

Answer is given below (on video)

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