Question

find the derivative of x.cosx by using the formulas of the derivatives.

Answer 1

Use the formula, d/dx(u*v) = u* d/dx(v) + v* d/dx(u)

d/dx(x*cosx)
= x* d/dx(cosx) + cosx* d/dx(x)
= x*(-sinx) + cosx * 1
= -x.sinx + cosx

Answer 2

Okay.... !! Let , y = xcosx ------(1) Using product rule , d/dx[f(x).g(x)] = f(x).d/dx{g(x)} + g(x).d/dx{f(x)} Differentiating equation 1 w.r.t. 'x' dy/dx = x(-sinx) + cosx dy/dx = cosx - xsinx