Question

How do you find the derivative of `y= 3^(2x+7)`?

Answer 1

`dy/dx=3^(2x+7)ln(9)`

Explanation:

Using the derivative `d/dxa^x = a^xln(a)` together with the chain rule, we can note that `3^(2x+7)` = `f(g(x))` where `f(x) = 3^x` and `g(x)=2x+7` and apply the chain rule to obtain:

`dy/dx = d/dx3^(2x+7)`

`=d/dxf(g(x))`

`=f'(g(x))g'(x)`

`=3^(2x+7)ln(3)*2`

`=3^(2x+7)ln(9)`