(\partial)/(\partial x)(4y*e^{5x^2-2y})

Lösung

\frac{\partial}{\partial x} (4 y \cdot e^{5 x^{2} - 2 y})

40 e^{5 x^{2} - 2 y} y x

Schritte zur Lösung

\frac{\partial}{\partial x} (4 y e^{5 x^{2} - 2 y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 y \frac{\partial}{\partial x} (e^{5 x^{2} - 2 y})

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (5 x^{2} - 2 y) = 10 x

= 4 y e^{5 x^{2} - 2 y} \cdot 10 x

Vereinfache

= 40 e^{5 x^{2} - 2 y} y x

\int_{1}^{4} 1 + \frac{1}{x ^{2}} d x

\frac{d}{d t} (- 3 cos^{2} (t) sin (t))

x \to 5 lim (x^{2})

x \to \infty lim ((x)!)

d er i v a t i v e π^{3}