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Derivative of cos x

ddx[cos⁡(x)]=−sin⁡(x)\frac{d}{dx}\left[\cos\left(x\right)\right] = -\sin\left(x\right)

Cosine starts at a peak, so its slope starts at 0 and turns negative, which is why the derivative is −sin x rather than +sin x.

Derivation

  1. Trig rule

    ddx[cos⁡(x)]=−sin⁡(x)\frac{d}{dx}\left[\cos\left(x\right)\right] = -\sin\left(x\right)
-4-3-2-11234-1-0.50.51
  • f(x) = cos x
  • f′(x)

Drag the graph · at x = 1.20 the slope is -0.93204, the height of the dashed curve.

Open in the derivative calculator

Questions students ask

What is the derivative of cos x?

ddx[cos⁡(x)]=−sin⁡(x)\frac{d}{dx}\left[\cos\left(x\right)\right] = -\sin\left(x\right).

How do you find the derivative of cos x?

Cosine starts at a peak, so its slope starts at 0 and turns negative, which is why the derivative is −sin x rather than +sin x.

What is the integral of cos x?

See the integral of cos x page for the antiderivative with steps.