derivative of x^2sin(x^2+3)

Lösung

\frac{d}{d x} (x^{2} sin (x^{2} + 3))

2 x sin (x^{2} + 3) + 2 x^{3} cos (x^{2} + 3)

Schritte zur Lösung

\frac{d}{d x} (x^{2} sin (x^{2} + 3))

Wende die Produktregel an:

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

f = x^{2}, g = sin (x^{2} + 3)

= \frac{d}{d x} (x^{2}) sin (x^{2} + 3) + \frac{d}{d x} (sin (x^{2} + 3)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (sin (x^{2} + 3)) = cos (x^{2} + 3) \cdot 2 x

= 2 x sin (x^{2} + 3) + cos (x^{2} + 3) \cdot 2 x x^{2}

cos (x^{2} + 3) \cdot 2 x x^{2} = 2 x^{3} cos (x^{2} + 3)

= 2 x sin (x^{2} + 3) + 2 x^{3} cos (x^{2} + 3)

\int \frac{1}{5 x + 8} d x

in v erse l a pl a ce \frac{2}{( s ) ( s + 2 )}

\int x^{2} - 25 d x

\frac{d}{d x} (sin^{2} (2 x + 1))

\frac{d}{d x} ((2 x - 1)^{2})