Question

What is the derivative of tan inverse of `(x^2 y^5)`?

Answer 1

`d/dx(tan^(-1)(x^2y^5))=1/(1+x^4y^10)[2xy^5+5x^2y^4(dy)/(dx)]`

Explanation:

We have to find derivative of `tan^(-1)(x^2y^5)`. For this we use the concept of chain rule for implicit differentiation as well as product rule..

Hence `d/dx(tan^(-1)(x^2y^5))`

= `1/(1+(x^2y^5)^2)[2x xxy^5+x^2xx5y^4xx(dy)/(dx)]`

= `1/(1+x^4y^10)[2xy^5+5x^2y^4(dy)/(dx)]`