# How do you differentiate 5xy + y^3 = 2x + 3y

How do you differentiate $5xy+{y}^{3}=2x+3y$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

recepiamsb
You can use implicit differentiation rememberig that y represents a function of x and needs to be differentiated accordingly;
for example: if you have ${y}^{2}$ you differentiate it to get:
$2y\cdot \frac{dy}{dx}$ where you use $\frac{dy}{dx}$ to take into account the dependence with x.
$5y+5x\frac{dy}{dx}+3{y}^{2}\frac{dy}{dx}=2+3\frac{dy}{dx}$
collect $\frac{dy}{dx}$
$\frac{dy}{dx}\left(5x+3{y}^{2}-3\right)=2-5y$
and
$\frac{dy}{dx}=\frac{2-5y}{5x+3{y}^{2}-3}$