derivative g(x)=3x^2log_{3}(x)

Lösung

ableitung von

g (x) = 3 x^{2} lo g_{3} (x)

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = lo g_{3} (x)

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

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

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{x ln ( 3 )}

= 3 (2 x lo g_{3} (x) + \frac{1}{x ln ( 3 )} x^{2})

Vereinfache

3 (2 x lo g_{3} (x) + \frac{1}{x ln ( 3 )} x^{2}) : \frac{3 ( x + 2 x ln ( x ) )}{ln ( 3 )}

= \frac{3 ( x + 2 x ln ( x ) )}{ln ( 3 )}

\frac{d}{d x} (\frac{x ^{3}}{e ^{2 x}})

\int \frac{4}{15} t^{\frac{5}{2}} + 2 cos (t) + Ct + C d t

n or ma l y = x^{3} - 3 x + 3, (3, 21)

t a y l or cos (4 x)

d er i v a t i v e csc (x) (x + cot (x))