Question

differentiate this please
dsin10t/
dt​

Answer 1

Substitution method

let 10t = u

du/dt = 10

→ dt = du/10

sin(10t) = sinu

→ dsin(10t)/dt

= d(sinu) ÷ (du/10)

= 10 × d(sinu)/u

= 10cosu

= 10cos(10t)

Or you can apply chain rule, differentiate sin10t in terms of 10t and then in terms of t

dsin(10t)/dt

= dsin(10t)/d(10t) × d(10t)/dt

= cos(10t) × 10

= 10cos(10t)