derivative of x^{cot(x})

Lösung

\frac{d}{d x} (x^{c o t (x)})

x^{c o t (x)} (- csc^{2} (x) ln (x) + \frac{cot ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{c o t (x)})

Wende Exponentenregel an:

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

x^{c o t (x)} = e^{c o t (x) l n (x)}

= \frac{d}{d x} (e^{c o t (x) l n (x)})

Wende die Kettenregel an:

e^{c o t (x) l n (x)} \frac{d}{d x} (cot (x) ln (x))

= e^{c o t (x) l n (x)} \frac{d}{d x} (cot (x) ln (x))

\frac{d}{d x} (cot (x) ln (x)) = - csc^{2} (x) ln (x) + \frac{cot ( x )}{x}

= e^{c o t (x) l n (x)} (- csc^{2} (x) ln (x) + \frac{cot ( x )}{x})

e^{c o t (x) l n (x)} = x^{c o t (x)}

= x^{c o t (x)} (- csc^{2} (x) ln (x) + \frac{cot ( x )}{x})

\frac{\partial}{\partial y} (sin (\frac{x}{y}))

\frac{d}{d x} (csc^{3} (3 - x))

\int \frac{8 x + 1}{( 4 x ^{2} + x ) ^{6}} d x

\frac{d}{d x} (8 7 x^{2} + 5)

\frac{d}{d x} (\frac{x}{x - 10})