What is implicit (x^2+4)y=8 ?

The answer to implicit (x^2+4)y=8 is (dy)/(dx)=-(2xy)/(x^2+4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

implicit (x^2+4)y=8

implicit derivative

(x^{2} + 4) y = 8

\frac{d y}{d x} = - \frac{2 x y}{x ^{2} + 4}

Solution steps

(x^{2} + 4) y = 8

Treat

y

y (x)

Differentiate both sides:

2 x y + \frac{d y}{d x} (x^{2} + 4) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{2 x y}{x ^{2} + 4}

\frac{d y}{d x} = - \frac{2 x y}{x ^{2} + 4}

\frac{\partial}{\partial y} (y - \frac{3}{x} + 1)

\int \frac{1}{x ( x ^{2} - 1 ) ^{\frac{3}{2}}} d x

6 e^{x} (cos (x) - sin (x))

\int_{7}^{14} 196 - x^{2} d x

\int \frac{1}{3} e^{x + 3} + \frac{3}{x} - 5 d x

What is implicit (x^2+4)y=8 ?
The answer to implicit (x^2+4)y=8 is (dy)/(dx)=-(2xy)/(x^2+4)