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Beliebt Rechnen >

(\partial)/(\partial y)(e^{1+x^2-y^2})

Lösung

\frac{\partial}{\partial y} (e^{1 + x^{2} - y^{2}})

Lösung

- 2 e^{1 + x^{2} - y^{2}} y

Schritte zur Lösung

\frac{\partial}{\partial y} (e^{1 + x^{2} - y^{2}})

Behandle

x

als Konstante

Wende die Kettenregel an:

e^{1 + x^{2} - y^{2}} \frac{\partial}{\partial y} (1 + x^{2} - y^{2})

= e^{1 + x^{2} - y^{2}} \frac{\partial}{\partial y} (1 + x^{2} - y^{2})

\frac{\partial}{\partial y} (1 + x^{2} - y^{2}) = - 2 y

= e^{1 + x^{2} - y^{2}} (- 2 y)

Vereinfache

= - 2 e^{1 + x^{2} - y^{2}} y

Beliebte Beispiele

derivative of 3/(x^4+2)

\frac{d}{d x} (\frac{3}{x ^{4} + 2})

tangent f(x)=x^2-1/x ,(2,3.5)

t an g e n t f (x) = x^{2} - \frac{1}{x}, (2, 3.5)

sum from n=1 to infinity}(((-7)^{n-1 of))/(8^n)

n = 1 \sum \infty \frac{( ( - 7 ) ^{n - 1} )}{8 ^{n}}

y^{''}-14y^'+49y=t^{-2}e^{7t}

y^{^{''}} - 14 y^{^{'}} + 49 y = t^{- 2} e^{7 t}

limit as x approaches-infinity of 7/x-4

x \to - \infty lim (\frac{7}{x} - 4)