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Beliebt Rechnen >

(\partial)/(\partial x)(bxe^{5xy})

Lösung

\frac{\partial}{\partial x} (b x e^{5 x y})

Lösung

b (e^{5 x y} + 5 e^{5 x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (b x e^{5 x y})

Behandle

b, y

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= b \frac{\partial}{\partial x} (x e^{5 x y})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{5 x y}

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{5 x y}) = e^{5 x y} \cdot 5 y

= b (1 \cdot e^{5 x y} + e^{5 x y} \cdot 5 y x)

Vereinfache

= b (e^{5 x y} + 5 e^{5 x y} x y)

Beliebte Beispiele

limit as x approaches (-1)+of 1/(x+1)

x \to (- 1) + lim (\frac{1}{x + 1})

limit as x approaches 2 of (4/x-2)/(x-2)

x \to 2 lim (\frac{\frac{4}{x} - 2}{x - 2})

(\partial)/(\partial x)(z^2)

\frac{\partial}{\partial x} (z^{2})

integral of (5x)/(5x^2+2)

\int \frac{5 x}{5 x ^{2} + 2} d x

derivative f(x)=e^6+ln(4)

d er i v a t i v e f (x) = e^{6} + ln (4)