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

Lösung

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

\frac{x + 2 x ln ( x )}{ln ( 10 )}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (lo g_{10} (x)) = \frac{1}{x ln ( 10 )}

= 2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2}

Vereinfache

2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2} : \frac{x + 2 x ln ( x )}{ln ( 10 )}

= \frac{x + 2 x ln ( x )}{ln ( 10 )}

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

\int_{1}^{\infty} x e^{- x} d x

\frac{d}{d x} (- \frac{1}{5} (x^{- 5} - x^{10}))

\frac{\partial}{\partial v} (u \cdot sin (v))

d er i v a t i v e f (x) = ∣ x - 2 ∣