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What is the derivative of the following function? f(x) = 4x^6/cos^5(x)

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Answer:


f'(x) = (24x^(5) \cos x + 20x^(6)\sin x)/(\cos^(6)x )

Explanation:

We have to find the derivative of the following function:


f(x) = (4x^(6) )/(\cos^(5) x )

Now, differentiating both sides with respect to x we get,


f'(x) = (\cos^(5)x (24x^(5)) - 4x^(6)(5\cos^(4)x )(- \sin x))/((\cos^(5)x )^(2))


f'(x) = ( 24x^(5) \cos x + 20 x^(6)\sin x)/(\cos^(6)x ) (Answer)

{Since, we know that,
(d(mx^(n) ))/(dx) = m * n x^((n - 1)) and
(d(\cos^(n) x))/(dx) = n \cos^((n - 1)) x(- \sin x) }

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