derivative of 2pix(cos(pix^2))

Lösung

\frac{d}{d x} (2 π x (cos (π x^{2})))

2 π (cos (π x^{2}) - 2 π x^{2} sin (π x^{2}))

Schritte zur Lösung

\frac{d}{d x} (2 π x (cos (π x^{2})))

Entferne die Konstante:

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

= 2 π \frac{d}{d x} (x cos (π x^{2}))

Wende die Produktregel an:

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

f = x, g = cos (π x^{2})

= 2 π (\frac{d x}{d x} cos (π x^{2}) + \frac{d}{d x} (cos (π x^{2})) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (cos (π x^{2})) = - sin (π x^{2}) \cdot 2 π x

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

Vereinfache

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

= 2 π (cos (π x^{2}) - 2 π x^{2} sin (π x^{2}))

d er i v a t i v e y = x^{5} e^{x}

n = 1 \sum \infty 4

n = 1 \sum \infty 0. 2^{n}

\int 15 x^{14} d x

\frac{\partial}{\partial z} (- 3 x y sin (z))