derivative f(x)=7sqrt(x)sin(x)

Lösung

ableitung von

f (x) = 7 x sin (x)

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

Schritte zur Lösung

\frac{d}{d x} (7 x sin (x))

Entferne die Konstante:

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

= 7 \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)

= 7 (\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)

= 7 (\frac{1}{2 x} sin (x) + cos (x) x)

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

= 7 (\frac{sin ( x )}{2 x} + x cos (x))

\int 49 tan^{5} (x) sec^{4} (x) d x

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\frac{x d y}{d x} = y^{2} - y

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