derivative of ln(x^2sin(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = ln (x^{2}), g = sin (x)

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

Vereinfache

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

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

\int \frac{( y ^{2} + 1 )}{y ^{2} + 4} d y

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

\frac{d}{d x} (x^{2} y^{4})

x \to 2 lim (x^{2} - 5)

x \to 0 lim (\frac{1 - e ^{- x}}{x})