find $\frac{dy}{dx}$. y = x^{-6} $\frac{dy}{dx}=square$

find $\frac{dy}{dx}$. y = x^{-6} $\frac{dy}{dx}=square$

find $\frac{dy}{dx}$. y = x^{-6} $\frac{dy}{dx}=square$

Answer

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = x^n$, then $\frac{dy}{dx}=nx^{n - 1}$. Here $n=-6$.

Step2: Calculate the derivative

Substitute $n = - 6$ into the power - rule formula: $\frac{dy}{dx}=-6x^{-6 - 1}$. Simplify the exponent: $\frac{dy}{dx}=-6x^{-7}$.

Answer:

$-6x^{-7}$