find the derivative of ( f(x) ).\n\n( f(x)=9 cdot 7^{x}+10 cdot 3^{x} )\n\n( f^{prime}(x)= )

Answer:

$9\cdot7^{x}\ln7 + 10\cdot3^{x}\ln3$

Explanation:

Step1: Differentiate term by term

Use the formula $\frac{d}{dx}(a\cdot b^{x})=a\cdot b^{x}\ln b$. For the first term $9\cdot7^{x}$: $$\frac{d}{dx}(9\cdot7^{x})=9\cdot7^{x}\ln7$$

Step2: Differentiate the second term

For the second term $10\cdot3^{x}$: $$\frac{d}{dx}(10\cdot3^{x})=10\cdot3^{x}\ln3$$

Step3: Sum the derivatives

$f^{\prime}(x)=\frac{d}{dx}(9\cdot7^{x})+\frac{d}{dx}(10\cdot3^{x}) = 9\cdot7^{x}\ln7 + 10\cdot3^{x}\ln3$