derivative y=3xln(x)

Lösung

ableitung von

y = 3 x ln (x)

3 (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (3 x ln (x))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (x ln (x))

Wende die Produktregel an:

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

f = x, g = ln (x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 3 (1 \cdot ln (x) + \frac{1}{x} x)

Vereinfache

3 (1 \cdot ln (x) + \frac{1}{x} x) : 3 (ln (x) + 1)

= 3 (ln (x) + 1)

\frac{\partial}{\partial x} (\frac{2 x - 2 y}{2 x + 2 y})

t an g e n t f (x) = \frac{9}{x}, at x = 2

\int_{1}^{5} x^{2} d x

\frac{d ^{2} y}{d x ^{2}} + y = 1 + x

\int (4 x^{3} - 9 x^{2} + 7 x) e^{- x} d x