Question

differentiate x^2 cosx with respect to x

Answer 1

let y = x^2cosx

and let 2cosx = t
now dydx = dy/dt×dt/dx

=> dy/dt = d/dt(x^t)
= tx^t-1 = 2cosx × x^2cosx-1

Now dt/dx = d/dx(2cosx)
= 2d/dx(cosx) = -2sinx
Hence
dy/dx = dy/dt×dt/dx
= (2cosx × x^2cosx-1)(-2sinx)
= -2.2sinxcosx. x^2COSx + 2sinx
= -2sin2x.x^2cosx + 2sinx
{ using sin2x = 2sinxcosx