Question

Differentiate the following:
y = 4 sec 5x

Answer 1

y = 4 sec 5x

[y = f(g(x)

${\displaystyle \frac{\text{d}y}{\text{d}x}}$ = f'(g(x)) . g'(x)]

${\displaystyle \frac{\text{d}y}{\text{d}x}=4\times \sec 5x\times \tan 5x\frac{\text{d}}{\text{d}x}\left(5x\right)}$

${\displaystyle \frac{\text{d}y}{\text{d}x}}$ = 4 sec 5x tan 5x × 5 × 1

${\displaystyle \frac{\text{d}y}{\text{d}x}}$ = 20 sec 5x tan 5x