Find $dy/dx$ for the equation below using implicit differentiation.
$5x^2+y^3=12$

$dy/dx=-$\frac{10x}{3y^2}$$

$dy/dx=$\frac{10x}{3y^2}$$

$dy/dx=$\left$(12-5x^2$\right$)^{$\left$($\frac$13$\right$)}$

$dy/dx=-$\left$(12-5x^2$\right$)^{$\left$($\frac$13$\right$)}$

Verified step by step guidance

Start with the given equation: 5x^2 + y^3 = 12.

Differentiate both sides of the equation with respect to x. Remember that y is a function of x, so use the chain rule for terms involving y.

The derivative of 5x^2 with respect to x is 10x.

For the term y^3, apply the chain rule: the derivative is 3y^2 * (dy/dx).

Set the derivatives equal to the derivative of the constant 12, which is 0, and solve for dy/dx: 10x + 3y^2 * (dy/dx) = 0. Rearrange to find dy/dx.

Master Finding The Implicit Derivative with a bite sized video explanation from Patrick

Problem sets built by lead tutors

Expert video explanations

Find dy/dxdy/dxdy/dx for the equation below using implicit differentiation.5x2+y3=125x^2+y^3=125x2+y3=12