Home > Calculus > Implicit Differentiation

How do you find #(dy)/(dx)# given #-2y^2+3=x^3#?

Answer 1

Charles Arocha

#\frac{dy}{dx}=-\frac{3x^2}{4y}#

Differentiate both sides as such: #\frac{d}{dx}(-2y^{2}+3)=\frac{d}{dx}(x^{3})# this leads to:

#-2\frac{d}{dx}(y^{2})=3x^{2}#

#-2(2y\frac{dy}{dx})=3x^{2}#

rearrange to make #\frac{dy}{dx}# the factor to get:

#\frac{dy}{dx}=-\frac{3x^{2}}{4y}#

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

Answer 2

Adam Adkins

To find (dy)/(dx) given the equation -2y^2 + 3 = x^3, we differentiate both sides of the equation with respect to x using implicit differentiation.

First, we differentiate -2y^2 + 3 with respect to y to find (dy)/(dx):

d/dx(-2y^2 + 3) = d/dx(x^3) -4y(dy/dx) = 3x^2

Next, solve for (dy)/(dx):

(dy/dx) = (3x^2) / (-4y)

Therefore, (dy)/(dx) = (3x^2) / (-4y).

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

Answer from HIX Tutor

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.