Question

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

Answer 1

`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)` }