derivative 2x^3+3log_{10}(x)+2sin(x)

Lösung

ableitung von

2 x^{3} + 3 lo g_{10} (x) + 2 sin (x)

6 x^{2} + \frac{3}{ln ( 10 ) x} + 2 cos (x)

Schritte zur Lösung

\frac{d}{d x} (2 x^{3} + 3 lo g_{10} (x) + 2 sin (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (3 lo g_{10} (x)) + \frac{d}{d x} (2 sin (x))

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

\frac{d}{d x} (3 lo g_{10} (x)) = \frac{3}{ln ( 10 ) x}

\frac{d}{d x} (2 sin (x)) = 2 cos (x)

= 6 x^{2} + \frac{3}{ln ( 10 ) x} + 2 cos (x)

d er i v a t i v e (1 + x^{2}) lo g_{2} (x)

\frac{d}{d t} (- 1 + cos^{2} (t))

d er i v a t i v e \frac{t ^{2}}{3}

d er i v a t i v e \frac{- 3}{x}

d er i v a t i v e \frac{1}{( x ^{3} + sin ( x ) ) ^{2}}