Answer:
[tex]f'(x) = \frac{24x^{5} \cos x + 20x^{6}\sin x}{\cos^{6}x }[/tex]
Step-by-step explanation:
We have to find the derivative of the following function:
[tex]f(x) = \frac{4x^{6} }{\cos^{5} x }[/tex]
Now, differentiating both sides with respect to x we get,
[tex]f'(x) = \frac{\cos^{5}x (24x^{5}) - 4x^{6}(5\cos^{4}x )(- \sin x)}{(\cos^{5}x )^{2}}[/tex]
⇒ [tex]f'(x) = \frac{ 24x^{5} \cos x + 20 x^{6}\sin x}{\cos^{6}x }[/tex] (Answer)
{Since, we know that, [tex]\frac{d(mx^{n} )}{dx} = m \times n x^{(n - 1)}[/tex] and [tex]\frac{d(\cos^{n} x)}{dx} = n \cos^{(n - 1)} x(- \sin x)[/tex] }
