derivative f(x)=4sqrt(x)sin(x)

Lösung

ableitung von

f (x) = 4 x sin (x)

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

Schritte zur Lösung

\frac{d}{d x} (4 x sin (x))

Entferne die Konstante:

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

= 4 \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)

= 4 (\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)

= 4 (\frac{1}{2 x} sin (x) + cos (x) x)

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

= 4 (\frac{sin ( x )}{2 x} + x cos (x))

\int cos^{2} (2 x) 2 d x

x \to 0 - lim (\frac{5}{x} - \frac{5}{x})

d er i v a t i v e sin (2 x + 1)

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

x \frac{d y}{d x} = y + (x^{2} - 4)^{2}