# How do you implicitly differentiate # y^2= x^3 + 3x^2 #?

It depends on what you are using as the independent variable. For

Solve for the derivative you're looking for.

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

To implicitly differentiate the equation (y^2 = x^3 + 3x^2), follow these steps:

- Differentiate both sides of the equation with respect to (x).
- Use the chain rule when differentiating (y^2) with respect to (x).
- Apply the power rule and chain rule when differentiating (x^3) and (3x^2), respectively.

The result of differentiating both sides with respect to (x) yields:

[2y \frac{dy}{dx} = 3x^2 + 6x]

Solve for (\frac{dy}{dx}) to obtain the implicit derivative:

[\frac{dy}{dx} = \frac{3x^2 + 6x}{2y}]

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 I differentiate #y=ln(sec(x) tan(x))#?
- What is the derivative of #7xy#?
- How do you implicitly differentiate #-y= x^3y^2-x^2y^3-2xy^4 #?
- How do you find the first and second derivatives of #y=(2x^4-3x)/(4x-1)# using the quotient rule?
- How do you differentiate #f(x) = (2x+1)^7# using the chain rule?

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