Answer
$y=12x-24$
Work Step by Step
The equation of the tangent line at $(2,0)$ is:
$$y=0+f'(2)(x-2)$$
Using the chain rule it follows:
$$f'(x)=(x^{3}-7)'\cdot \frac{1}{x^{3}-7}$$
$$f'(x)=3x^{2}\cdot \frac{1}{x^{3}-7}$$
$$f'(x)=\frac{3x^{2}}{x^{3}-7}$$
$$f'(2)=\frac{3\cdot 2^{2}}{2^{3}-7}$$
$$f'(2)=12$$
so:
$$y=0+f'(2)(x-2)$$
$$y=0+12(x-2)$$
$$y=12x-24$$
