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Beliebt Rechnen >

implicit (dy)/(dx),x=e^y

Lösung

implizite ableitung

\frac{d y}{d x}, x = e^{y}

Lösung

\frac{d y}{d x} = \frac{1}{e ^{y}}

Schritte zur Lösung

x = e^{y}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

1 = e^{y} \frac{d y}{d x}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{e ^{y}}

\frac{d y}{d x} = \frac{1}{e ^{y}}

Beliebte Beispiele

integral of 5/(4+9t^2)

\int \frac{5}{4 + 9 t ^{2}} d t

y^3-(18x+6)+3xy^2y^'=0

y^{3} - (18 x + 6) + 3 x y^{2} y^{^{'}} = 0

derivative of 6x^2e^{-x}

\frac{d}{d x} (6 x^{2} e^{- x})

y^{''}+4y=2e^x+sin(2x)

y^{^{''}} + 4 y = 2 e^{x} + sin (2 x)

(\partial)/(\partial y)((x^2+y^2)/(x^2-y^2))

\frac{\partial}{\partial y} (\frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}})