(\partial)/(\partial x)(2xcos(x^2+y^2))

Lösung

\frac{\partial}{\partial x} (2 x cos (x^{2} + y^{2}))

2 (cos (x^{2} + y^{2}) - 2 x^{2} sin (x^{2} + y^{2}))

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x cos (x^{2} + y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = cos (x^{2} + y^{2})

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

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

\frac{\partial}{\partial x} (cos (x^{2} + y^{2})) = - sin (x^{2} + y^{2}) \cdot 2 x

= 2 (1 \cdot cos (x^{2} + y^{2}) + (- sin (x^{2} + y^{2}) \cdot 2 x) x)

Vereinfache

2 (1 \cdot cos (x^{2} + y^{2}) + (- sin (x^{2} + y^{2}) \cdot 2 x) x) : 2 (cos (x^{2} + y^{2}) - 2 x^{2} sin (x^{2} + y^{2}))

= 2 (cos (x^{2} + y^{2}) - 2 x^{2} sin (x^{2} + y^{2}))

\frac{d y}{d t} = yr (1000 - y)

a re a y = sec^{2} (x), y = 8 cos (x), - \frac{π}{3}, \frac{π}{3}

\int_{1}^{\infty} \frac{ln ( x )}{x ^{\frac{3}{2}}} d x

\frac{d}{d x} (1000 (1 + \frac{x}{12})^{60})

d er i v a t i v e f (x) = (1 - x) (x^{2} - 7)^{2}