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Beliebt Rechnen >

derivative of e^{x^y}

Lösung

\frac{d}{d x} (e^{x^{y}})

Lösung

e^{x^{y}} x^{y} (ln (x) \frac{d y}{d x} + \frac{y}{x})

Schritte zur Lösung

\frac{d}{d x} (e^{x^{y}})

Wende die Kettenregel an:

e^{x^{y}} \frac{d}{d x} (x^{y})

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

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

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

Beliebte Beispiele

derivative of e^{x^2}sin(x^3-2)

\frac{d}{d x} (e^{x^{2}} sin (x^{3} - 2))

y^{''}+25y=30sin(5t)

y^{^{''}} + 25 y = 30 sin (5 t)

derivative of ln(x+sqrt(x^2-12))

\frac{d}{d x} (ln (x + x^{2} - 12))

(x^4+2x^3y^2)dx+x^4ydy=0

(x^{4} + 2 x^{3} y^{2}) d x + x^{4} y d y = 0

(dy)/(dt)-2y=3e^{-2t},y(0)=10

\frac{d y}{d t} - 2 y = 3 e^{- 2 t}, y (0) = 10