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3.5

Implicit Differentiation

Derivatives of Inverse Trigonometric Functions

$$\begin{gathered} \frac{d}{dx}\left({\sin }^{-1}x\right) = \frac{1}{\sqrt{1-x^2}} \\ \frac{d}{dx}\left({\cos }^{-1}x\right) =- \frac{1}{\sqrt{1-x^2}} \\ \frac{d}{dx}\left({\tan }^{-1}x\right) =\frac{1}{1+x^2} \\ \frac{d}{dx}\left(cs{c}^{-1}x\right) =- \frac{1}{x\sqrt{x^2-1}} \\ \frac{d}{dx}\left(se{c}^{-1}x\right) = \frac{1}{x\sqrt{x^2-1}} \\ \frac{d}{dx}\left(co{t}^{-1}x\right) = -\frac{1}{x + x^2} \end{gathered}$$

The derivatives of the inverse trigonometric functions are on the table. Remember, anything that starts with "co-" has a negative derivative.

Links

• Home
• 3.1: Derivatives of Polynomials and Exponential Functions
• 3.2: The Product and Quotient Rules
• 3.3: Derivatives of Trigonometric Functions
• 3.4: The Chain Rule
• 3.5: Implicit Differentiation
• 3.6: Steps in Logarithmic Differentiation
• 3.7: Rates of Change in the Natural and Social Sciences
• 3.8: Exponential Growth and Decay
• 3.9: Related Rates
• 3.10: Linear Approximations and Differentials
• 3.11: Hyperbolic Functions