Question

Finding second Derivatives In Exercise,find the second derivate.
f(x) = 2e3x + 3e - 2x

Answer 1

Answer: The second derivative would be
`f''(x)=18e^(3x)+12e^(-2x)`

Explanation:

Since we have given that

`f(x)=2e^(3x)+3e^(-2x)`

We will first find the first derivative w.r.t 'x'.

As we know that

`e^(mx)=me^x\\\\e^(-nx)=-ne^(-nx)`

So, it becomes,

`f'(x)=6e^(3x)-6xe^(-2x)`

Now, the second derivative w.r.t 'x' would be

`f''(x)=6* 3e^(3x)-6* -2e^(-2x)=18e^(3x)+12e^(-2x)`

Hence, the second derivative would be
`f''(x)=18e^(3x)+12e^(-2x)`