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Beliebt Rechnen >

(\partial)/(\partial x)(e^{7x^2+5y^2})

Lösung

\frac{\partial}{\partial x} (e^{7 x^{2} + 5 y^{2}})

Lösung

e^{7 x^{2} + 5 y^{2}} \cdot 14 x

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{7 x^{2} + 5 y^{2}})

Behandle

y

als Konstante

Wende die Kettenregel an:

e^{7 x^{2} + 5 y^{2}} \frac{\partial}{\partial x} (7 x^{2} + 5 y^{2})

= e^{7 x^{2} + 5 y^{2}} \frac{\partial}{\partial x} (7 x^{2} + 5 y^{2})

\frac{\partial}{\partial x} (7 x^{2} + 5 y^{2}) = 14 x

= e^{7 x^{2} + 5 y^{2}} \cdot 14 x

Beliebte Beispiele

tangent f(x)=4x^2-2x+1

t an g e n t f (x) = 4 x^{2} - 2 x + 1

tangent f(x)=sqrt(2x+1),\at x=3

t an g e n t f (x) = 2 x + 1, at x = 3

slopeintercept (-1,-1),(1,5)

s l o p e in t erce pt (- 1, - 1), (1, 5)

derivative of (3x-1^4(2x+1)^{-3})

\frac{d}{d x} ((3 x - 1)^{4} (2 x + 1)^{- 3})

xy^'-y=x^2+5x-1

x y^{^{'}} - y = x^{2} + 5 x - 1