Question

(v) sin 4x cosx what is the defferentiation​

Answer 1

Answer:

let, y = sin^4(x) + cos^4(x)

Differentiating both side w.r.t x and applying chain rule

dy/dx = 4sin^3(x)cos(x) - 4cos^3(x)sin(x)

= 4sin(x)cos(x){sin^2(x) - cos^2(x)}

= 2* 2sin(x)cos(x) [ - {cos^2(x) - sin^2(x)}]

= - 2 sin(2x)[cos(2x)]

= - 2 sin(2x)cos(2x)

= - sin(4x)

** Formula used