derivative f(x)=x^2sin(sqrt(x))

Lösung

ableitung von

f (x) = x^{2} sin (x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

\frac{cos ( x )}{2 x} x^{2} = \frac{x ^{\frac{3}{2}} cos ( x )}{2}

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

\int x + 8 d x

\frac{d}{d x} (x^{2} - 27)

\int ((4 x + 3) (2 x^{2} + 3 x)^{3}) d x

\frac{d ^{2}}{d x ^{2}} ((9 x^{2} + 6)^{7})

s l o p e (- 2.5) (- 4.1)