Question

find the derivative of the following function. f(x)=7x^5 + 9x f(x)=□

Explanation:

Step1: Apply power - rule to first term

The power - rule for differentiation is $\frac{d}{dx}(ax^n)=nax^{n - 1}$. For the term $7x^5$, $a = 7$ and $n = 5$. So, $\frac{d}{dx}(7x^5)=5\times7x^{5 - 1}=35x^4$.

Step2: Apply power - rule to second term

For the term $9x$, $a = 9$ and $n = 1$. Using the power - rule $\frac{d}{dx}(9x)=1\times9x^{1 - 1}=9$.

Step3: Sum the derivatives of the terms

Since the derivative of a sum of functions is the sum of their derivatives, $f'(x)=\frac{d}{dx}(7x^5)+\frac{d}{dx}(9x)$. So, $f'(x)=35x^4 + 9$.

Answer:

$35x^4+9$