Question

find the derivative of the following function. g(w)=2w^5 + 7w^2+13w g(w)=□

Explanation:

Step1: Apply power - rule to first term

The power - rule for differentiation is $\frac{d}{dw}(aw^n)=naw^{n - 1}$. For the term $2w^5$, $n = 5$ and $a = 2$. So, $\frac{d}{dw}(2w^5)=5\times2w^{5 - 1}=10w^4$.

Step2: Apply power - rule to second term

For the term $7w^2$, $n = 2$ and $a = 7$. So, $\frac{d}{dw}(7w^2)=2\times7w^{2 - 1}=14w$.

Step3: Apply power - rule to third term

For the term $13w$, $n = 1$ and $a = 13$. So, $\frac{d}{dw}(13w)=1\times13w^{1 - 1}=13$.

Step4: Sum up the derivatives of each term

$g'(w)=\frac{d}{dw}(2w^5)+\frac{d}{dw}(7w^2)+\frac{d}{dw}(13w)=10w^4 + 14w+13$.

Answer:

$10w^4 + 14w + 13$