Question

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

y = x3x+1

Answer 1

`(dy)/(dx)=3x^(3x)(lnx+1)`

Explanation:

We are given that a function

`y=x^(3x)+1`

We have to find the derivative of the function

Let
`u=x^(3x)`

`y=u+1`

Taking ln on both sides

`lnu=3xln x`

By using
`lna^b=blna`

Differentiate w.r.t x

`(1)/(u)(du)/(dx)=3(lnx+x* (1)/(x))=3(lnx+1)`

`(d(lnx))/(dx)=(1)/(x)`

`(d(u\cdot v))/(dx)=u'v+v'u`

`(du)/(dx)=3u(lnx+1)=3x^(3x)(lnx+1)`

Differentiate y w.r.t x

`(dy)/(dx)=(du)/(dx)`

Using the value of du/dx

`(dy)/(dx)=3x^(3x)(lnx+1)`