derivative 5x^3log_{3}(x)

Lösung

ableitung von

5 x^{3} lo g_{3} (x)

\frac{5 ( x ^{2} + 3 x ^{2} ln ( x ) )}{ln ( 3 )}

Schritte zur Lösung

\frac{d}{d x} (5 x^{3} lo g_{3} (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x^{3} lo g_{3} (x))

Wende die Produktregel an:

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

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

= 5 (\frac{d}{d x} (x^{3}) lo g_{3} (x) + \frac{d}{d x} (lo g_{3} (x)) x^{3})

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

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

= 5 (3 x^{2} lo g_{3} (x) + \frac{1}{x ln ( 3 )} x^{3})

Vereinfache

5 (3 x^{2} lo g_{3} (x) + \frac{1}{x ln ( 3 )} x^{3}) : \frac{5 ( x ^{2} + 3 x ^{2} ln ( x ) )}{ln ( 3 )}

= \frac{5 ( x ^{2} + 3 x ^{2} ln ( x ) )}{ln ( 3 )}

\int 0.8 sin (x) + \frac{1.6}{π ^{2}} x d x

\frac{\partial}{\partial z} (tan (5 + 2 x^{2} y^{4} z^{2}))

\frac{d y}{d x} = 5^{t a n (5 x)}

y^{^{''}} - \frac{2}{t ^{2}} y = 0

\frac{\partial}{\partial x} (x^{3} sin (x^{2}))