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Popular >

implicit (dy)/(dx),1+ln(9xy)=e^{(9x-y)}

Solution

implicit derivative

\frac{d y}{d x}, 1 + ln (9 x y) = e^{(9 x - y)}

Solution

\frac{d y}{d x} = \frac{9 e ^{9 x - y} x y - y}{x ( 1 + e ^{- y + 9 x} y )}

Solution steps

1 + ln (9 x y) = e^{9 x - y}

Treat

y

as

y (x)

Differentiate both sides:

\frac{x \frac{d y}{d x} + y}{x y} = e^{9 x - y} (9 - \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{9 e ^{9 x - y} x y - y}{x ( 1 + e ^{- y + 9 x} y )}

\frac{d y}{d x} = \frac{9 e ^{9 x - y} x y - y}{x ( 1 + e ^{- y + 9 x} y )}

Popular Examples

integral of (31)/(x(x^2+4)^2)

\int \frac{31}{x ( x ^{2} + 4 ) ^{2}} d x

derivative of (7w^{10}-11w^7)/(8w^7)derivative of

\frac{7 w ^{10} - 11 w ^{7}}{8 w ^{7}}

integral of 19arctan(sqrt(x))

\int 19 arctan (x) d x

limit as x approaches-2+of-3x^2+2

x \to - 2 + lim (- 3 x^{2} + 2)

derivative of x^{sqrt(x)}derivative of

x^{x}

Frequently Asked Questions (FAQ)

What is implicit (dy)/(dx),1+ln(9xy)=e^{(9x-y)} ?
The answer to implicit (dy)/(dx),1+ln(9xy)=e^{(9x-y)} is (dy)/(dx)=(9e^{9x-y}xy-y)/(x(1+e^{-y+9x)y)}