derivative of (ln(x+3x)^2)

Lösung

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

\frac{2 ln ( x )}{x} + 6 ln (x) + 6 + 18 x

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 (ln (x) + 3 x) (\frac{1}{x} + 3) : \frac{2 ln ( x )}{x} + 6 ln (x) + 6 + 18 x

= \frac{2 ln ( x )}{x} + 6 ln (x) + 6 + 18 x

\frac{\partial}{\partial x} (ln (x + 9 y + 2 z))

\frac{d}{d x} (2 tan (x + \frac{π}{12}))

\frac{d}{d x} ((x + 1)^{\frac{2}{3}} (3 x^{2} - 2)^{3})

\int (sec (2 x) tan (2 x)) d x

\int \frac{m ^{3}}{( z ^{2} ) ^{3}} d m