Trig Function Derivatives

This purely reference page lists the derivatives of the trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

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$Tip icon$ Notice that a negative sign appears in the derivatives of the co-functions: cosine, cosecant, and cotangent.

Sine

The derivative of sine is cosine.

$𝑓 (𝑥) = s i n (𝑥) \Rightarrow 𝑓' (𝑥) = c o s (𝑥)$

The derivative of cosine is negative sine.

$𝑓 (𝑥) = c o s (𝑥) \Rightarrow 𝑓' (𝑥) = - s i n (𝑥)$

The derivative of tangent is secant squared.

$𝑓 (𝑥) = t a n (𝑥) \Rightarrow 𝑓' (𝑥) = s e c 2 (𝑥)$

The derivative of cotangent is negative cosecant squared.

$𝑓 (𝑥) = c o t (𝑥) \Rightarrow 𝑓' (𝑥) = - c s c 2 (𝑥)$

The derivative of secant is secant times tangent.

$𝑓 (𝑥) = s e c (𝑥) \Rightarrow 𝑓' (𝑥) = s e c (𝑥) t a n (𝑥)$

The derivative of cosecant is negative cosecant times cotangent.

$𝑓 (𝑥) = c s c (𝑥) \Rightarrow 𝑓' (𝑥) = - c s c (𝑥) c o t (𝑥)$

To practice using the rules above, visit our free Derivatives of sin x and cos x page.