Essential Concepts
- We can find the derivatives of [latex]\sin x[/latex] and [latex]\cos x[/latex] by using the definition of derivative and the limit formulas found earlier. The results are
[latex]\frac{d}{dx} \sin x= \cos x[/latex] and [latex]\frac{d}{dx} \cos x=−\sin x[/latex].
- With these two formulas, we can determine the derivatives of all six basic trigonometric functions.
Key Equations
- Derivative of sine function
[latex]\frac{d}{dx}(\sin x)= \cos x[/latex] - Derivative of cosine function
[latex]\frac{d}{dx}(\cos x)=−\sin x[/latex] - Derivative of tangent function
[latex]\frac{d}{dx}(\tan x)=\sec^2 x[/latex] - Derivative of cotangent function
[latex]\frac{d}{dx}(\cot x)=−\csc^2 x[/latex] - Derivative of secant function
[latex]\frac{d}{dx}(\sec x)= \sec x \tan x[/latex] - Derivative of cosecant function
[latex]\frac{d}{dx}(\csc x)=−\csc x \cot x[/latex]
