derivative of sin(x^2cos(pix+2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = sin (x^{2}), g = cos (π x + 2)

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

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

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

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

Vereinfache

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

\frac{\partial}{\partial y} (4 x^{3} - 36 x)

\int 4 y e^{y^{2}} d y

s l o p e in t erce pt (1999, 67%), (2005, 92%)

t a y l or x^{5}, 1

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