What is implicit (dy)/(dx),(7xy+5)^2=42y ?

The answer to implicit (dy)/(dx),(7xy+5)^2=42y is (dy)/(dx)=-(y(7xy+5))/(7x^2y+5x-3)

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implicit (dy)/(dx),(7xy+5)^2=42y

implicit derivative

\frac{d y}{d x}, (7 x y + 5)^{2} = 42 y

\frac{d y}{d x} = - \frac{y ( 7 x y + 5 )}{7 x ^{2} y + 5 x - 3}

Solution steps

(7 x y + 5)^{2} = 42 y

Treat

y

y (x)

Differentiate both sides:

14 (7 x y + 5) (x \frac{d y}{d x} + y) = 42 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ( 7 x y + 5 )}{7 x ^{2} y + 5 x - 3}

\frac{d y}{d x} = - \frac{y ( 7 x y + 5 )}{7 x ^{2} y + 5 x - 3}

\frac{d}{d x} (\frac{x}{( 5 x - 4 ) ^{3}})

t \to 0 lim (\frac{( 2 e ^{t} - 2 )}{t})

d er i v a t i v e e^{x} x

x \to 0 + lim (x^{2} sin (\frac{1}{x}))

\frac{\partial}{\partial y} (4 y^{3} - 100 y)

What is implicit (dy)/(dx),(7xy+5)^2=42y ?
The answer to implicit (dy)/(dx),(7xy+5)^2=42y is (dy)/(dx)=-(y(7xy+5))/(7x^2y+5x-3)