Question

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

y = e^x^2 ln 4x^3

Answer 1

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

Answer:

`(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))`

Explanation:

We are given that a function

`y=e^(x^2)ln(4x^3)`

We have to differentiate w.r.t x

`(dy)/(dx)=e^(x^2)* 2xln(4x^3)+e^(x^2)* (1)/(4x^3)* 12x^2`

By using formula

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

`(d(e^x))/(dx)=e^x`

`(dy)/(dx)=e^(x^2)(2xln(4x^3)+(3)/(x))`

`(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))`

Hence, the derivative of function

`(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))`