# What is the derivative of #sin^3(x)cos(x)#?

Here We use: Product Rule , Power Rule and Differentiation of Trigonometric Functions

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of ( \sin^3(x)\cos(x) ), use the product rule and the chain rule:

[ \frac{d}{dx} (\sin^3(x)\cos(x)) = 3\sin^2(x)\cos(x)\frac{d}{dx}(\sin(x)) + \sin^3(x)(-\sin(x))\frac{d}{dx}(\cos(x)) ]

[ = 3\sin^2(x)\cos(x)\cos(x) + \sin^3(x)(-\sin(x))(-\sin(x)) ]

[ = 3\sin^2(x)\cos^2(x) - \sin^4(x)\cos(x) ]

So, the derivative of ( \sin^3(x)\cos(x) ) is ( 3\sin^2(x)\cos^2(x) - \sin^4(x)\cos(x) ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7