Answered: "Find the derivatives of the functions s=cos4(1−2t)" - Plainmath

nicekikah

Answered question

2021-10-05

Find the derivatives of the functions

s = \cos^{4} (1 - 2 t)

Answer & Explanation

StrycharzT

Skilled2021-10-06Added 102 answers

Step 1
Given:

s (t) = \cos^{4} (1 - 2 t)

we know that

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

...(1)

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

...(2)
Step 2
so, by using equation(1) and equation(2)

s^{'} (t) = \frac{d}{d t} (\cos^{4} (1 - 2 t))

= 4 \cos^{3} (1 - 2 t) \frac{d}{d t} (\cos (1 - 2 t))

= 4 \cos^{3} (1 - 2 t) (- \sin (1 - 2 t)) \frac{d}{d t} (1 - 2 t)

= - 4 \sin (1 - 2 t) \cos^{3} (1 - 2 t) (0 - 2)

= 8 \sin (1 - 2 t) \cos^{3} (1 - 2 t)

hence, derivative of given function is

8 \sin (1 - 2 t) \cos^{3} (1 - 2 t)

.

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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