Derivative Rules - Trigonometric Angle with Power as Fraction (with Rule) to Derivative

Question

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

$$\begin{array}{l} \displaystyle \frac{d}{dx}\sin\left(u\right) = \cos\left(u\right) \cdot \frac{du}{dx} \[12pt] \displaystyle f(x) = \sin\left(\frac{1}{x^{2}}\right) \end{array}$$

Accepted Answer

$$f'(x) = \cos\left(\frac{1}{x^{2}}\right) \cdot \left(-\frac{2}{x^{3}}\right)$$

Answer

$$f'(x) = \sin\left(\frac{1}{x^{2}}\right) \cdot \left(-\frac{2}{x^{3}}\right)$$

Answer

$$f'(x) = \cos\left(\frac{1}{x^{2}}\right) \cdot (\frac{1}{x^{2}})$$

Answer

$$f'(x) = \cos\left(\frac{1}{x^{2}}\right)$$

Derivative Rules - Trigonometric Angle with Power as Fraction (with Rule) to Derivative

Practice:

Derivative Rules - Trigonometric Angle with Power as Fraction (with Rule) to Derivative