derivative (x^2)/(tan(x))

Lösung

ableitung von

\frac{x ^{2}}{tan ( x )}

2 x cot (x) - x^{2} csc^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{tan ( x )})

Vereinfache

\frac{x ^{2}}{tan ( x )} : x^{2} cot (x)

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

Wende die Produktregel an:

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

f = x^{2}, g = cot (x)

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

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

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

= 2 x cot (x) + (- csc^{2} (x)) x^{2}

Vereinfache

= 2 x cot (x) - x^{2} csc^{2} (x)

d er i v a t i v e y = 4 cos (4 x^{2})

d er i v a t i v e \frac{1}{( 2 x + 1 )}

d er i v a t i v e \frac{ln ( 1 )}{x}

d er i v a t i v e (6 x^{2} + 11)^{\frac{1}{2}}

d er i v a t i v e 3 x^{2} - 1