# How to find the derivative of #3arccos(x/2)#?

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

To find the derivative of ( 3\arccos(x/2) ), you can use the chain rule. The derivative of ( \arccos(u) ) with respect to ( u ) is ( -\frac{1}{\sqrt{1 - u^2}} ), and the derivative of ( u = \frac{x}{2} ) with respect to ( x ) is ( \frac{1}{2} ). Applying the chain rule, the derivative is:

[ \frac{d}{dx} [3\arccos(x/2)] = 3 \times \left( -\frac{1}{\sqrt{1 - (x/2)^2}} \right) \times \frac{d}{dx} \left( \frac{x}{2} \right) ] [ = -\frac{3}{\sqrt{1 - (x/2)^2}} \times \frac{1}{2} ] [ = -\frac{3}{2\sqrt{1 - (x/2)^2}} ]

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