Summary of Derivatives of Trigonometric Functions | Calculus I

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Module 3: Derivatives

Summary of Derivatives of Trigonometric Functions

Essential Concepts

We can find the derivatives of $\sin x$ and $\cos x$ by using the definition of derivative and the limit formulas found earlier. The results are
$\frac{d}{dx} \sin x= \cos x$ and $\frac{d}{dx} \cos x=−\sin x$ .
With these two formulas, we can determine the derivatives of all six basic trigonometric functions.

Key Equations

Derivative of sine function
$\frac{d}{dx}(\sin x)= \cos x$
Derivative of cosine function
$\frac{d}{dx}(\cos x)=−\sin x$
Derivative of tangent function
$\frac{d}{dx}(\tan x)=\sec^2 x$
Derivative of cotangent function
$\frac{d}{dx}(\cot x)=−\csc^2 x$
Derivative of secant function
$\frac{d}{dx}(\sec x)= \sec x \tan x$
Derivative of cosecant function
$\frac{d}{dx}(\csc x)=−\csc x \cot x$