I got 3x^2/x^3-7 but I'm not sure where to go from there.
Also I ran into this problem and haven't been able to figure it out. Thanks for your time, I really appreciate it.
2026-03-16 10:41:19.1773657679
Derivatives with ln Issues
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Hint: Use the chain rule: $$\dfrac{d}{dx}f(g(x))=f^\prime(g(x))g^\prime(x)$$ Then, the tangent to the graph of $f(g(x))$ at $(x_1,y_1=f(g(x_1)))$ is $$y-f(g(x_1))=f^\prime(g(x_1))g^\prime(x_1)(x-x_1)\\ \implies y=xf^\prime(g(x_1))g^\prime(x_1)-x_1f^\prime(g(x_1))g^\prime(x_1)+f(g(x_1))$$ Let me show you as an example the first one: $$\dfrac{dy}{dx}=\dfrac{3x^2}{x^3-7}\\ \implies \left.\dfrac{dy}{dx}\right|_{x=2}=12\\ \implies y=xf^\prime(g(x_1))g^\prime(x_1)-x_1f^\prime(g(x_1))g^\prime(x_1)+f(g(x_1))\\ \implies y=12x-24$$