5. (3 pts) Consider the following functions. Find the derivatives with Form 2 of the chain rule. Do not take the time to simplify your answers. a. \( f(x)=\frac{5\left(x^{4}-3^{x}\right)^{2}}{7} \) b. \( g(x)=\frac{-17}{\sqrt[3]{3 x^{2}-2 x+5}} \) c. \( h(x)=2 e^{x^{2}-5}+\ln \left(x^{-3}\right)-7 \sqrt{x} \)

To find the derivatives of the given functions using Form 2 of the chain rule, you can follow this method: For \( f(x) = \frac{5\left(x^{4}-3^{x}\right)^{2}}{7} \): \[ f'(x) = \frac{5}{7} \cdot 2\left(x^4 - 3^x\right) \cdot \left(4x^3 - 3^x \ln(3)\right) \] For \( g(x) = \frac{-17}{\sqrt[3]{3 x^{2}-2 x+5}} \): Using the chain rule on the cube root gives: \[ g'(x) = -17 \cdot \left(-\frac{1}{3}\right)(3 x^2 - 2 x + 5)^{-\frac{2}{3}} \cdot (6x - 2) \] For \( h(x) = 2 e^{x^{2}-5}+\ln \left(x^{-3}\right)-7 \sqrt{x} \): The derivative is: \[ h'(x) = 2 e^{x^2 - 5} \cdot (2x) + \frac{-3}{x} - \frac{7}{2\sqrt{x}} \] These derivatives give you a sense of how the functions change with respect to \(x\)!