Question

find the derivative of the function.
k(x) = -9(6x² + 7)⁻⁶
k’(x) = \square

Explanation:

Step1: Apply chain rule

Let $u=6x^2+7$, so $k(x)=-9u^{-6}$. Derivative: $k'(x)=-9\cdot(-6)u^{-7}\cdot u'$

Step2: Compute $u'$

$u'=\frac{d}{dx}(6x^2+7)=12x$

Step3: Substitute back $u$

$k'(x)=54(6x^2+7)^{-7}\cdot12x = 648x(6x^2+7)^{-7}$

Answer:

$648x(6x^2 + 7)^{-7}$