# What is the derivative of #arcsin(x^2/4)#?

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

To find the derivative of ( \arcsin{\left(\frac{x^2}{4}\right)} ), we can use the chain rule.

[ \frac{d}{dx} \left( \arcsin{\left(\frac{x^2}{4}\right)} \right) = \frac{1}{\sqrt{1 - \left(\frac{x^2}{4}\right)^2}} \cdot \frac{d}{dx} \left(\frac{x^2}{4}\right) ]

Using the chain rule, we differentiate the inner function ( \frac{x^2}{4} ) with respect to ( x ):

[ \frac{d}{dx} \left(\frac{x^2}{4}\right) = \frac{1}{4} \cdot 2x = \frac{x}{2} ]

Now, substituting this into our derivative expression:

[ \frac{d}{dx} \left( \arcsin{\left(\frac{x^2}{4}\right)} \right) = \frac{1}{\sqrt{1 - \left(\frac{x^2}{4}\right)^2}} \cdot \frac{x}{2} ]

Therefore, the derivative of ( \arcsin{\left(\frac{x^2}{4}\right)} ) with respect to ( x ) is ( \frac{x}{2\sqrt{4 - x^4}} ).

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