derivative of x^{sin^2(x})

Lösung

\frac{d}{d x} (x^{s i n^{2} (x)})

x^{s i n^{2} (x)} (sin (2 x) ln (x) + \frac{sin ^{2} ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{s i n^{2} (x)})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{s i n^{2} (x)} = e^{s i n^{2} (x) l n (x)}

= \frac{d}{d x} (e^{s i n^{2} (x) l n (x)})

Wende die Kettenregel an:

e^{s i n^{2} (x) l n (x)} \frac{d}{d x} (sin^{2} (x) ln (x))

= e^{s i n^{2} (x) l n (x)} \frac{d}{d x} (sin^{2} (x) ln (x))

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

= e^{s i n^{2} (x) l n (x)} (sin (2 x) ln (x) + \frac{sin ^{2} ( x )}{x})

e^{s i n^{2} (x) l n (x)} = x^{s i n^{2} (x)}

= x^{s i n^{2} (x)} (sin (2 x) ln (x) + \frac{sin ^{2} ( x )}{x})

\frac{d}{d a} (\frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}})

\frac{\partial}{\partial x} (5)

\frac{d y}{d x} - \frac{( y ^{2} - x ^{2} )}{3 x y} = 0

\int 3 x^{4} + 2 x^{2} - \frac{x}{2} d x

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