Question

Finding a derivative: use the rule of differentiation to find the derivative of the functiony = 3/x^7

Answer 1

Given the function:

$y=\frac{3}{x^7}$

Let's use the rule of differentiation to find the derivative of the function.

To find the derivative using the rule of differentiation, we have:

Since 3 is constant with respect to x, we have:

$3\frac{dy}{dx}(\frac{1}{x^7})$

Apply the basic rule of exponents:

$3\frac{d}{dx}(x^{-7})$

Differentiate using Power rule:

$\begin{gathered} 3(-7x^{-8}) \\ \\ =-21x^{-8} \end{gathered}$

Apply the negative exponent rule:

$=-\frac{21}{x^8}$

Therefore, the derivative of the function is:

$\frac{dy}{dx}=-\frac{21}{x^8}$

ANSWER:

$\frac{dy}{dx}=-\frac{21}{x^{8}}$