What is implicit (dy)/(dx),4^x=2xy ?

The answer to implicit (dy)/(dx),4^x=2xy is (dy}{dx}=\frac{ln(2)*4^x-y)/x

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implicit (dy)/(dx),4^x=2xy

implicit derivative

\frac{d y}{d x}, 4^{x} = 2 x y

\frac{d y}{d x} = \frac{ln ( 2 ) \cdot 4 ^{x} - y}{x}

Solution steps

4^{x} = 2 x y

Treat

y

y (x)

Differentiate both sides:

ln (2) \cdot 2^{2 x + 1} = 2 (y + x \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{ln ( 2 ) \cdot 4 ^{x} - y}{x}

\frac{d y}{d x} = \frac{ln ( 2 ) \cdot 4 ^{x} - y}{x}

\int \frac{x}{x + 4} d x

(x + y) d x + (x - y) d y = 0

\int_{0}^{8} π (1 - \frac{y}{8})^{2} d y

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

\int sin^{7} (\frac{3}{5} x) d x

What is implicit (dy)/(dx),4^x=2xy ?
The answer to implicit (dy)/(dx),4^x=2xy is (dy}{dx}=\frac{ln(2)*4^x-y)/x