If f(x) = (x)(4^x), what is the simplified second derivative?

First find f’(x) using the product rule.

The product rule shows how to find the derivative of two terms being multiplied together. The formula is: f(x) = xy, f’(x) =(x)(y’)+(y)(x’)

The derivative of a^x = a^x(lna)

The derivative of x(4^x) is (x)(4^x(ln4))+(4^x)
which can be written as 4^x(ln(4)(x) +1)

To take the f’’(x), use the product rule again.
4^x(ln(4)) + (ln(4)(x) + 1)(4^xln4). You can factor out 4^x(ln(4)) to get 4^xln(4)(ln(4)(x)+1+1))

1+1=2. The final simplified answer is (4^xln(4))(ln(4)(x)+2). I don’t think you can simplify anymore