derivative x^2cos(log_{10}(x))

Lösung

ableitung von

x^{2} cos (lo g_{10} (x))

2 x cos (lo g_{10} (x)) - \frac{x sin ( lo g _{10} ( x ) )}{ln ( 10 )}

Schritte zur Lösung

\frac{d}{d x} (x^{2} cos (lo g_{10} (x)))

Wende die Produktregel an:

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

f = x^{2}, g = cos (lo g_{10} (x))

= \frac{d}{d x} (x^{2}) cos (lo g_{10} (x)) + \frac{d}{d x} (cos (lo g_{10} (x))) x^{2}

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

\frac{d}{d x} (cos (lo g_{10} (x))) = - \frac{sin ( lo g _{10} ( x ) )}{ln ( 10 ) x}

= 2 x cos (lo g_{10} (x)) + (- \frac{sin ( lo g _{10} ( x ) )}{ln ( 10 ) x}) x^{2}

Vereinfache

2 x cos (lo g_{10} (x)) + (- \frac{sin ( lo g _{10} ( x ) )}{ln ( 10 ) x}) x^{2} : 2 x cos (lo g_{10} (x)) - \frac{x sin ( lo g _{10} ( x ) )}{ln ( 10 )}

= 2 x cos (lo g_{10} (x)) - \frac{x sin ( lo g _{10} ( x ) )}{ln ( 10 )}

\frac{d}{d t} (2 t - 2)

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