Question: "Find the derivative of f(x)=x6cos⁡xf'(x)=" - Plainmath

iohanetc

Answered question

2021-09-25

Find the derivative of

f (x) = x^{6} \cos x

f'(x)=

Answer & Explanation

d2saint0

Skilled2021-09-26Added 89 answers

Step 1
Given:

f (x) = x^{6} \cos x

To find: f'(x)
Using product rule of derivatives, (f.g)' = f.g' + f'.g where f and g are functions
Step 2
So,

f (x) = x^{6} \cos x

gives,

f^{'} (x) = x^{6} (- \sin x) + (6 x^{5}) \cos x

Since, we know that

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

and

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

So,

f^{'} (x) = x^{6} (- \sin x) + (6 x^{5}) \cos x

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