# How do you use the chain rule to differentiate #y=-5/(3x^2-4)^6#?

Applying the chain rule:

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

To differentiate ( y = -5/(3x^2 - 4)^6 ) using the chain rule:

- Identify the outer function: ( u = -5u^6 )
- Find the inner function: ( u = 3x^2 - 4 )
- Differentiate the inner function: ( \frac{du}{dx} = 6(3x^2 - 4)^5(6x) )
- Substitute the inner function and its derivative into the outer function: ( \frac{dy}{dx} = \frac{du}{dx} \cdot \frac{dy}{du} )
- Simplify the expression: ( \frac{dy}{dx} = 6(3x^2 - 4)^5(6x) \cdot -\frac{5}{(3x^2 - 4)^6} )
- Further simplify if needed.

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.

- How do you differentiate # f(x)=ln(x^2-x)# using the chain rule.?
- How do you differentiate #y=(e^(2x)+1)^3#?
- How do you differentiate #f(x)=ln(sinx)/cosx# using the quotient rule?
- How do you find the first and second derivatives of #f(x)=(x)/(x^2+1)# using the quotient rule?
- How do you find the derivative using quotient rule of #[x(3x+5)] / (1-x^2)#?

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