Question

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

Answer 1

Answer:

$f'(x) = \frac{24x^{5} \cos x + 20x^{6}\sin x}{\cos^{6}x }$

Step-by-step explanation:

We have to find the derivative of the following function:

$f(x) = \frac{4x^{6} }{\cos^{5} x }$

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

$f'(x) = \frac{\cos^{5}x (24x^{5}) - 4x^{6}(5\cos^{4}x )(- \sin x)}{(\cos^{5}x )^{2}}$

⇒ $f'(x) = \frac{ 24x^{5} \cos x + 20 x^{6}\sin x}{\cos^{6}x }$ (Answer)

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