Question

find the derivative of the function.
y = \frac{8}{x^{5}} - \frac{2}{x^{4}}+\frac{4}{x}+\sqrt{6}
\frac{dy}{dx}=□

Explanation:

Step1: Rewrite terms with negative exponents

$y = 8x^{-5}-2x^{-4}+4x^{-1}+\sqrt{6}$

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: $\frac{d}{dx}(8x^{-5})=-40x^{-6}$
For the second term: $\frac{d}{dx}(-2x^{-4}) = 8x^{-5}$
For the third term: $\frac{d}{dx}(4x^{-1})=-4x^{-2}$
For the fourth term: $\frac{d}{dx}(\sqrt{6}) = 0$ (since the derivative of a constant is 0)

Step3: Combine the derivatives

$\frac{dy}{dx}=-40x^{-6}+8x^{-5}-4x^{-2}$

Answer:

$- \frac{40}{x^{6}}+\frac{8}{x^{5}}-\frac{4}{x^{2}}$