determine the derivative of (f(x)=4^{x}). solution: we get (f(x)=4^{x}ln(4)). evaluate (int 2^{x}dx)…

determine the derivative of (f(x)=4^{x}). solution: we get (f(x)=4^{x}ln(4)). evaluate (int 2^{x}dx). solution: we get (int 2^{x}dx=\frac{2^{x}}{ln(2)}+c). determine the derivative of (f(x)=5^{x}).

determine the derivative of (f(x)=4^{x}). solution: we get (f(x)=4^{x}ln(4)). evaluate (int 2^{x}dx). solution: we get (int 2^{x}dx=\frac{2^{x}}{ln(2)}+c). determine the derivative of (f(x)=5^{x}).

Answer

Explanation:

Step1: Recall derivative formula

The derivative of $y = a^{x}$ is $y'=a^{x}\ln(a)$. For $f(x)=5^{x}$, here $a = 5$.

Step2: Calculate the derivative

Using the formula, $f'(x)=5^{x}\ln(5)$.

Answer:

$f'(x)=5^{x}\ln(5)$