"Find the derivatives of the functions defined as..." solved and explained - Plainmath

Falak Kinney

Answered question

2021-10-23

Find the derivatives of the functions defined as follows.

y = \frac{1}{2} \sin 8 x

Answer & Explanation

Roosevelt Houghton

Skilled2021-10-24Added 106 answers

Step 1
The given function is

y = \frac{1}{2} \sin 8 x

.
Differentiate y with respect to x.

y^{'} = \frac{d}{d x} (\frac{1}{8} \sin 8 x)

= \frac{1}{8} \frac{d}{d x} (\sin 8 x)

Step 2
Use the differentiation formula,

\frac{d}{d x} \sin x = \cos x and \frac{d}{d x} x^{n} = n x^{n - 1}

.

\frac{1}{8} \frac{d}{d x} (\sin 8 x) = \frac{1}{8} \cos 8 x \frac{d}{d x} (8 x)

= \frac{1}{8} \cos 8 x (8)

= \cos 8 x

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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