# How do you find the derivative of #arcsin(4x)#?

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

To find the derivative of (y = \arcsin(4x)), use the chain rule. The derivative of (\arcsin(u)) with respect to (u) is (\frac{1}{\sqrt{1-u^2}}), and then you multiply by the derivative of (u) with respect to (x), where (u = 4x).

So, start with:

[y = \arcsin(4x)]

Taking the derivative of both sides with respect to (x), we get:

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

[ \frac{dy}{dx} = \frac{1}{\sqrt{1-16x^2}} \cdot 4 ]

[ \frac{dy}{dx} = \frac{4}{\sqrt{1-16x^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