find the derivative of the function. y = 3 / x ^ 4 - 3 / x dy / dx = □

Explanation:

Step1: Rewrite the function

Rewrite $y = \frac{3}{x^{4}}-\frac{3}{x}$ as $y = 3x^{-4}-3x^{-1}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $\frac{dy}{dx}=anx^{n - 1}$. For the first term $3x^{-4}$, $a = 3$ and $n=-4$. So its derivative is $3\times(-4)x^{-4 - 1}=-12x^{-5}$. For the second term $-3x^{-1}$, $a=-3$ and $n = - 1$. So its derivative is $-3\times(-1)x^{-1 - 1}=3x^{-2}$.

Step3: Combine the derivatives

$\frac{dy}{dx}=-12x^{-5}+3x^{-2}$.

Answer:

$- \frac{12}{x^{5}}+\frac{3}{x^{2}}$