What is implicit x^5+x^2y^3=0 ?

The answer to implicit x^5+x^2y^3=0 is (dy)/(dx)=-(5x^3+2y^3)/(3xy^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

implicit x^5+x^2y^3=0

implicit derivative

x^{5} + x^{2} y^{3} = 0

\frac{d y}{d x} = - \frac{5 x ^{3} + 2 y ^{3}}{3 x y ^{2}}

Solution steps

x^{5} + x^{2} y^{3} = 0

Treat

y

y (x)

Differentiate both sides:

5 x^{4} + 2 x y^{3} + 3 y^{2} \frac{d y}{d x} x^{2} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{5 x ^{3} + 2 y ^{3}}{3 x y ^{2}}

\frac{d y}{d x} = - \frac{5 x ^{3} + 2 y ^{3}}{3 x y ^{2}}

What is implicit x^5+x^2y^3=0 ?
The answer to implicit x^5+x^2y^3=0 is (dy)/(dx)=-(5x^3+2y^3)/(3xy^2)