Question

differentiate.
y = - \frac{70}{x^{6}}
\frac{d}{dx} \left( - \frac{70}{x^{6}} \
ight) = \square

Explanation:

Step1: Rewrite the function

Rewrite \(y =-\frac{70}{x^{6}}\) as \(y=-70x^{- 6}\) using the rule \(\frac{1}{a^{n}}=a^{-n}\).

Step2: Apply the power rule

The power rule for differentiation is \(\frac{d}{dx}(x^{n})=nx^{n - 1}\).
For \(y = - 70x^{-6}\), we have \(\frac{dy}{dx}=-70\times(-6)x^{-6 - 1}\).

Step3: Simplify the expression

\(-70\times(-6)x^{-7}=\frac{420}{x^{7}}\)

Answer:

\(\frac{420}{x^{7}}\)