Question

Find the derivastive of the following functions with respect to x. a. `y=x^2 sinx, b. `y= (sin x)/x and c. y=sin (x^2)`

Answer 1

`y=x^2 sin x`
`dy/dx= x^2 d/dx(sinx)+(sinx) d/dx (x^2)`
`=x^2cosx+(sinx)(2x)`
`=x(2sinx+x cosx)` b. `y=(sinx)/2`
dy/dx= (x d/dx(sinx) - sin x(dx/dy))/x^2`
`=(x cosx-sinx)/x^2`
`dy/dx=d/dx^2(sinx^2).(d(x^2))/dx`
`=2x cos x^2`.