What is implicit (dy)/(dx),x^3+y^3=36 ?

The answer to implicit (dy)/(dx),x^3+y^3=36 is (dy)/(dx)=-(x^2)/(y^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

implicit (dy)/(dx),x^3+y^3=36

implicit derivative

\frac{d y}{d x}, x^{3} + y^{3} = 36

\frac{d y}{d x} = - \frac{x ^{2}}{y ^{2}}

Solution steps

x^{3} + y^{3} = 36

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

\frac{d y}{d x} = - \frac{x ^{2}}{y ^{2}}

What is implicit (dy)/(dx),x^3+y^3=36 ?
The answer to implicit (dy)/(dx),x^3+y^3=36 is (dy)/(dx)=-(x^2)/(y^2)