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Trig Function Derivatives

Handy Table of Trig Function Derivatives

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\begin{align*}
\frac{d}{dx}\left(\sin x\right) &= \cos x \\[8px]
\dfrac{d}{dx}\left(\cos x\right) &= -\sin x \\[8px]
\dfrac{d}{dx}\left(\tan x\right) &= \sec^2 x \\[8px]
\frac{d}{dx}\left(\csc x\right) &= -\csc x \cot x \\[8px]
\frac{d}{dx}\left(\sec x\right) &= \sec x \tan x \\[8px]
\frac{d}{dx}\left(\cot x\right) &= -\csc^2 x
\end{align*}

In words:

  • The derivative of sin(x) is cos(x).
  • The derivative of cos(x) is –sin(x).
  • The derivative of tan(x) is [sec(x)]^2.
  • The derivative of csc(x) is –csc(x)cot(x).
  • The derivative of sec(x) is sec(x)tan(x).
  • The derivative of cot(x) is –[csc(x)]^2.

Tips iconNotice that a negative sign appears in the derivatives of the co-functions: cosine, cosecant, and cotangent.