(\partial)/(\partial x)(x^{sin(x)})

Lösung

\frac{\partial}{\partial x} (x^{s i n (x)})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{s i n (x)})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

6 \cdot (\frac{d y}{d x}) = y^{2}, y (0) = 4

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

y^{^{'}} = \frac{( x ^{2} y - y )}{y + 1}

\frac{\partial}{\partial x} (4 x^{4} y^{8} + 9 x^{6} y^{7})

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