find the derivative of the function.\ny = \\frac{6}{x^{5}}-\\frac{3}{x}\n\\frac{dy}{dx}=\\square
find the derivative of the function.\ny = \\frac{6}{x^{5}}-\\frac{3}{x}\n\\frac{dy}{dx}=\\square
Answer
Explanation:
Step1: Rewrite the function
Rewrite $y = \frac{6}{x^{5}}-\frac{3}{x}$ as $y = 6x^{-5}-3x^{-1}$.
Step2: Apply power - rule for derivatives
The power - rule states that if $y = ax^{n}$, then $\frac{dy}{dx}=anx^{n - 1}$. For the first term $y_1 = 6x^{-5}$, $\frac{dy_1}{dx}=6\times(-5)x^{-5 - 1}=-30x^{-6}$. For the second term $y_2=-3x^{-1}$, $\frac{dy_2}{dx}=-3\times(-1)x^{-1 - 1}=3x^{-2}$.
Step3: Find the derivative of the whole function
Since $y = y_1 + y_2$, $\frac{dy}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}=-30x^{-6}+3x^{-2}$.
Answer:
$- \frac{30}{x^{6}}+\frac{3}{x^{2}}$