Question

How do you find the second derivative of `f(x)=ln(7x^2e^x\sin x)`?

Answer 1

`(d^2f) /(dx^2)=-2/x^2-csc^2x`

Explanation:

As `f(x)=ln(7x^2e^xsinx)`

i.e. `f(x)=ln7+2lnx+x+lnsinx`

Hence `(df)/(dx)=2/x+1+1/sinx*cosx`

= `2/x+1+cotx`

or `(d^2f) /(dx^2)=-2/x^2-csc^2x`