Question

Differentiate the functions with respect to x.
$cos\ x^3.sin^2(x^5)$

Answer 1

The given function is cos x3 . sin2(x5)

$\frac {d}{dx}$[cos x3. sin2(x5)] = sin2(x5) . $\frac {d}{dx}$(cos x3) + cos x3 . $\frac {d}{dx}$[sin2(x5)]
= sin2(x5) . (- sin x3) . $\frac {d}{dx}$(x3) + cos x3 . 2 sin (x5) . $\frac {d}{dx}$(sin x5)
= -sin x3 sin2(x5) . 3x2 + 2 sin x5 cos x3 . cos x5. $\frac {d}{dx}$(x5)
= -3x2 sin x3 . sin2(x5) + 2 sin x5 cos x5 cos x3.5x4
= 10x4 sin x5 cos x5 cos x3 - 3x2 sinx3 cosx3 sin2(x5)