# How do you use the chain rule to differentiate #y=(-5x^3-3)^3#?

change u back into terms of x

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

To differentiate ( y=(-5x^3-3)^3 ) using the chain rule:

- Identify the outer function, which is ( u^3 ), where ( u = -5x^3 - 3 ).
- Differentiate the outer function with respect to ( u ) to get ( \frac{dy}{du} = 3u^2 ).
- Identify the inner function, which is ( -5x^3 - 3 ).
- Differentiate the inner function with respect to ( x ) to get ( \frac{du}{dx} = -15x^2 ).
- Apply the chain rule: Multiply ( \frac{dy}{du} ) and ( \frac{du}{dx} ).
- Substitute ( u = -5x^3 - 3 ) back into the result.

The derivative of ( y=(-5x^3-3)^3 ) is ( \frac{dy}{dx} = 3(-5x^3 - 3)^2(-15x^2) ).

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

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