What is implicit (dy)/(dx),(3xy+7)^2=6y ?

The answer to implicit (dy)/(dx),(3xy+7)^2=6y is (dy)/(dx)=-(y(3xy+7))/(3x^2y+7x-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

implicit (dy)/(dx),(3xy+7)^2=6y

implicit derivative

\frac{d y}{d x}, (3 x y + 7)^{2} = 6 y

\frac{d y}{d x} = - \frac{y ( 3 x y + 7 )}{3 x ^{2} y + 7 x - 1}

Solution steps

(3 x y + 7)^{2} = 6 y

Treat

y

y (x)

Differentiate both sides:

6 (3 x y + 7) (x \frac{d y}{d x} + y) = 6 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ( 3 x y + 7 )}{3 x ^{2} y + 7 x - 1}

\frac{d y}{d x} = - \frac{y ( 3 x y + 7 )}{3 x ^{2} y + 7 x - 1}

\int sec^{2} (θ) tan^{2} (θ) d θ

y^{^{''}} + 62 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int_{- 1}^{1} 4 - x^{2} d x

\frac{d y}{d x} = x (e + y)

y = - x^{2}

What is implicit (dy)/(dx),(3xy+7)^2=6y ?
The answer to implicit (dy)/(dx),(3xy+7)^2=6y is (dy)/(dx)=-(y(3xy+7))/(3x^2y+7x-1)