Question

What is the derivative of `f(x)=e^(4x)*ln(1-x)` ?

Answer 1

`y'=e^(4x)(4ln(1-x)-1/(1-x))`

Explanation:

`f(x)=e^(4x)⋅ln(1−x)`

Suppose, `y=f(x)*g(x)`

In general Product Rule is,

`y'=f(x)*g'(x)+f'(x)*g(x)`

Assume, `f(x)=e^(4x)` and `g(x)=ln(1-x)`

differentiating these functions with respect to `x`, we get

`f'(x)=4*e^(4x)`

and `g'(x)=-1/(1-x)`

Plugging these in product rule definition yields,

`y'=e^(4x)(-1/(1-x))+(4*e^(4x))ln(1-x)`

`y'=e^(4x)(4ln(1-x)-1/(1-x))`