Question

differentiate
1.sin^2t(sint)
2.sin^3t

Answer 1

we know,
a function is product of two functions f(x) and g(x) .
e.g y = f(x).g(x)
differentiate wrt x
dy/dx = f(x) × dg(x)/dx + g(x).df(x)/dx

use this concept for solving first question.

(1) y = sin²t ( sint)
differentiate wrt t

dy/dt = sin²t .d(sint)/dt + sint.d(sin²t)/dt
= sin²t .cost + sint.2sint × cost
=3sin²t.cost

(2) y = sin³t
y = (sint)³
differentiate wrt t
dy/dt = d(sint)³/dt
=3(sint)² × d(sint)/dt
=3sin²t.cost