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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

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

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

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

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

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

\int (z + 1) e^{z} d z

x \to 0 + lim (\frac{2}{x} - \frac{1}{ln ( x )})

\int_{1}^{\infty} e^{- 2 x} d x

\frac{\partial}{\partial x} (x^{4 y})

x y^{^{'}} = 2 y + 7 x