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
