The derivative of cos cube x (cos^3x) is equal to -3cos^{2}x sinx. In this post, we will find the derivative of cos cube x using the chain rule.

The derivative formula of cos^{3}x is given as follows:

d/dx (cos^{3}x) = -3cos^{2}x sinx.

## Derivative of Cos^3x

The derivative of cos^{3}x is -3cos^{2}x sinx. |

**Explanation:**

As cos^{3}x is a composite function, we will use the chain rule to find its derivative. To do so, let us put

u = cosx.

Thus, cos^{3}x = u^{3}.

As u=cosx, we have that du/dx = -sinx.

Now, by the chain rule the derivative of cos cube x will be equal to

$\dfrac{d}{dx}$ (cos^{3}x) = $\dfrac{d}{dx}$ (u^{3})

= $\dfrac{d}{du}$ (u^{3}) × $\dfrac{du}{dx}$

= 3u^{2} × (-sinx) by the power rule of derivatives: d/dx (x^{n}) =nx^{n-1}.

= – 3cos^{2}x sinx.

So the derivative of cos^{3}x (cos cube x) is equal to – 3cos^{2}x sinx, that is, d/dx (cos^{3}x) = -3cos^{2}x sinx which is proved by the chain rule of derivatives.

**Have You Read These Derivatives?**

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Derivative of π | Derivative of e^{1/x} |

## FAQs

**Q1: What is the derivative of cos ^{3}x?**

**Answer:** The derivative of cos^{3}x (cos cube x) is – 3cos^{2}x sinx.

**Q1: If y=cos ^{3}x, then find dy/dx?**

**Answer:** If y=cos^{3}x, then dy/dx = -3cos^{2}x sinx.