Question

find the derivative of the function.
y = \frac{2}{x^{7}} - \frac{5}{x}
\frac{dy}{dx} = box

Explanation:

Step1: Rewrite the function

Rewrite $y = \frac{2}{x^{7}}-\frac{5}{x}$ as $y = 2x^{-7}-5x^{-1}$.

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $\frac{dy}{dx}=nax^{n - 1}$.
For the first term $y_1 = 2x^{-7}$, $\frac{dy_1}{dx}=2\times(-7)x^{-7 - 1}=-14x^{-8}$.
For the second term $y_2 = - 5x^{-1}$, $\frac{dy_2}{dx}=-5\times(-1)x^{-1 - 1}=5x^{-2}$.

Step3: Find the derivative of the whole function

Since $\frac{dy}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}$, we have $\frac{dy}{dx}=-14x^{-8}+5x^{-2}$.

Answer:

$- \frac{14}{x^{8}}+\frac{5}{x^{2}}$