Derivative Rules - Multi Chain Quotient Trigonometric to Derivative

Question

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

$$f(x) = \frac{\sqrt{(x^{2} + 5)}}{4\sin(x)}$$

Accepted Answer

$$f'(x) = \frac{\frac{1}{2}(x^{2} + 5)^{-\frac{1}{2}}(2x)\left(4\sin(x)\right) - \sqrt{(x^{2} + 5)}\left(4\cos(x)\right)}{\left(4\sin(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{\sqrt{(x^{2} + 5)}\left(4\cos(x)\right) - \frac{1}{2}(x^{2} + 5)^{-\frac{1}{2}}(2x)\left(4\sin(x)\right)}{\left(4\sin(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{\frac{1}{2}(x^{2} + 5)^{-\frac{1}{2}}(2x)\left(4\sin(x)\right) + \sqrt{(x^{2} + 5)}\left(4\cos(x)\right)}{\left(4\sin(x)\right)^{2}}$$

Answer

$$f'(x) = \frac{\frac{1}{2}(x^{2} + 5)^{-\frac{1}{2}}(2x)\left(4\sin(x)\right) - \sqrt{(x^{2} + 5)}\left(4\cos(x)\right)}{4\sin(x)}$$

Derivative Rules - Multi Chain Quotient Trigonometric to Derivative

Practice:

Derivative Rules - Multi Chain Quotient Trigonometric to Derivative