derivative f(x)=5sqrt(x)sin(x)

Lösung

ableitung von

f (x) = 5 x sin (x)

5 (\frac{sin ( x )}{2 x} + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (5 x sin (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x sin (x))

Wende die Produktregel an:

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

f = x, g = sin (x)

= 5 (\frac{d}{d x} (x) sin (x) + \frac{d}{d x} (sin (x)) x)

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= 5 (\frac{1}{2 x} sin (x) + cos (x) x)

\frac{1}{2 x} sin (x) = \frac{sin ( x )}{2 x}

= 5 (\frac{sin ( x )}{2 x} + x cos (x))

\int_{0}^{π} cos (2 x) d x

\int \frac{x}{x ^{2} - 3} d x

in v erse l a pl a ce \frac{1}{x ( x ^{2} + 2 x + x )}

\frac{d}{d x} (\frac{1}{6 x + 5})

\frac{\partial}{\partial y} (7 ln (2 x^{5} - 3 y))