derivative sqrt(ln(x^2+4)+xsin(2x))

Lösung

ableitung von

ln (x^{2} + 4) + x sin (2 x)

\frac{2 x + sin ( 2 x ) ( x ^{2} + 4 ) + 2 x cos ( 2 x ) ( x ^{2} + 4 )}{2 ( x ^{2} + 4 ) ln ( x ^{2} + 4 ) + x sin ( 2 x )}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} + 4) + x sin (2 x))

Wende die Kettenregel an:

\frac{1}{2 ln ( x ^{2} + 4 ) + x sin ( 2 x )} \frac{d}{d x} (ln (x^{2} + 4) + x sin (2 x))

= \frac{1}{2 ln ( x ^{2} + 4 ) + x sin ( 2 x )} \frac{d}{d x} (ln (x^{2} + 4) + x sin (2 x))

\frac{d}{d x} (ln (x^{2} + 4) + x sin (2 x)) = \frac{2 x}{x ^{2} + 4} + sin (2 x) + 2 x cos (2 x)

= \frac{1}{2 ln ( x ^{2} + 4 ) + x sin ( 2 x )} (\frac{2 x}{x ^{2} + 4} + sin (2 x) + 2 x cos (2 x))

Vereinfache

\frac{1}{2 ln ( x ^{2} + 4 ) + x sin ( 2 x )} (\frac{2 x}{x ^{2} + 4} + sin (2 x) + 2 x cos (2 x)) : \frac{2 x + sin ( 2 x ) ( x ^{2} + 4 ) + 2 x cos ( 2 x ) ( x ^{2} + 4 )}{2 ( x ^{2} + 4 ) ln ( x ^{2} + 4 ) + x sin ( 2 x )}

= \frac{2 x + sin ( 2 x ) ( x ^{2} + 4 ) + 2 x cos ( 2 x ) ( x ^{2} + 4 )}{2 ( x ^{2} + 4 ) ln ( x ^{2} + 4 ) + x sin ( 2 x )}

\frac{d}{d x} (6 x^{2} + 8 x + 6)

\int x^{15} e^{- x^{8}} d x

\int (2 x + 5) (x^{2} + 5 x)^{7} d x

\frac{d y}{d x} = \frac{13 x y}{( ln ( y ) ) ^{10}}

y^{^{'}} = \frac{5 y}{x + 3}