derivative of 4xln(x)

Lösung

\frac{d}{d x} (4 x ln (x))

4 (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (4 x ln (x))

Entferne die Konstante:

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

= 4 \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)

= 4 (\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}

= 4 (1 \cdot ln (x) + \frac{1}{x} x)

Vereinfache

4 (1 \cdot ln (x) + \frac{1}{x} x) : 4 (ln (x) + 1)

= 4 (ln (x) + 1)

t an g e n t f (x) = x^{2} + x, at x = - 4

\int_{0}^{1} e^{x} d x

ma c l a u r in e^{x^{2}}

\int \frac{x ^{2} - 7}{( x - 2 ) ( x + 1 )} d x

\int \frac{cot ^{2} ( x )}{sin ^{2} ( x )} d x