find the derivative of the function. y = 7 / x ^ 4 - 4 / x dy / dx = □

Explanation:

Step1: Rewrite the function

Rewrite $y = \frac{7}{x^{4}}-\frac{4}{x}$ as $y = 7x^{-4}-4x^{-1}$.

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $\frac{dy}{dx}=anx^{n - 1}$. For $y_1 = 7x^{-4}$, $\frac{dy_1}{dx}=7\times(-4)x^{-4 - 1}=-28x^{-5}$. For $y_2=-4x^{-1}$, $\frac{dy_2}{dx}=-4\times(-1)x^{-1 - 1}=4x^{-2}$.

Step3: Find the derivative of the whole function

Since $y = y_1 + y_2$, $\frac{dy}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}=-28x^{-5}+4x^{-2}$.

Answer:

$- \frac{28}{x^{5}}+\frac{4}{x^{2}}$