Question

Find dy/dx , if y = e^x^2+2 + sin (5x^2+2) + 3 cos^2x?

Answer 1

`dy/dx=2xe^{x^2+2}+10x\cos(5x^2+2)-3\sin2x`

Explanation:

Given function:

`y=e^{x^2+2}+\sin(5x^2+2)+3\cos^2x`

differentiating above equation w.r.t. `x` using chain rule as follows

`dy/dx=d/dx(e^{x^2+2})+d/dx\sin(5x^2+2)+3d/dx\cos^2x`

`=e^{x^2+2}d/dx(x^2+2)+\cos(5x^2+2)d/dx(5x^2+2)+3(2\cos x)d/dx(\cosx)`

`=e^{x^2+2}(2x)+\cos(5x^2+2)(10x)+3(2\cos x)(-\sinx)`

`=2xe^{x^2+2}+10x\cos(5x^2+2)-3\sin2x`