# How do you use the chain rule to differentiate #y=(-3x^5+1)^3#?

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

The chain rule states that:

Hmm... What does that mean?

To use the chain rule, we need to find the inside function and the outside function.

Using the power rule:

We do the similar thing with the inside function.

Now, we put the original inside function inside the derivative of the outside function.

We multiply this by the derivative of the inside function.

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

To differentiate ( y=(-3x^5+1)^3 ) using the chain rule, follow these steps:

- Identify the inner function ( u ) as ( -3x^5+1 ).
- Find its derivative ( \frac{du}{dx} ), which is ( -15x^4 ).
- Raise the inner function to the power of 2, yielding ( u^2 = (-3x^5+1)^2 ).
- Multiply by the derivative of the inner function: ( 2(-3x^5+1)(-15x^4) ).
- This gives the derivative of the outer function with respect to the inner function: ( \frac{d}{du} [u^3] = 3u^2 ).
- Substitute ( u = -3x^5+1 ) back in: ( 3(-3x^5+1)^2 ).
- Finally, multiply by the derivative of the inner function: ( 3(-3x^5+1)^2 \cdot (-15x^4) ).

So, the derivative of ( y=(-3x^5+1)^3 ) is ( \frac{dy}{dx} = 3(-3x^5+1)^2 \cdot (-15x^4) ).

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

- If #f(x)= 2x - e^x # and #g(x) = 3 x #, how do you differentiate #f(g(x)) # using the chain rule?
- How do you find the derivative of #y=x(x^2+1)#?
- How do you differentiate #f(x)=e^x*e^(1/x) # using the product rule?
- How do you differentiate #f(x)=tan(sqrt(x^3-1)) # using the chain rule?
- How do you differentiate #f(x)= (4 x^2 + 2x -3 )/ (x- 1 )# using the quotient rule?

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