Derivative Rules - Multi Chain Quotient Trigonometric (with Rule) to Derivative

Question

Find the derivative f'(x) using the quotient, chain, and trigonometric rules.

$$\begin{array}{l} \displaystyle \text{if } h(x) = \frac{f(x)}{g(x)},\ h'(x) = \frac{f'(x)\,g(x) - f(x)\,g'(x)}{[g(x)]^{2}} \[12pt] \displaystyle f(x) = \frac{(x + 2)^{3}}{\sin(x)} \end{array}$$

Accepted Answer

$$f'(x) = \frac{3(x + 2)^{2}\left(\sin(x)\right) - (x + 2)^{3}\left(\cos(x)\right)}{\left(\sin(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{(x + 2)^{3}\left(\cos(x)\right) - 3(x + 2)^{2}\left(\sin(x)\right)}{\left(\sin(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{3(x + 2)^{2}\left(\sin(x)\right) - (x + 2)^{3}\left(\cos(x)\right)}{\sin(x)}$$

Answer

$$f'(x) = \frac{3(x + 2)^{2}\left(\sin(x)\right) + (x + 2)^{3}\left(\cos(x)\right)}{\left(\sin(x)\right)^{2}}$$

Derivative Rules - Multi Chain Quotient Trigonometric (with Rule) to Derivative

Practice:

Derivative Rules - Multi Chain Quotient Trigonometric (with Rule) to Derivative