derivative of xcoth(1+x^2)

Lösung

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

coth (1 + x^{2}) - 2 x^{2} csch^{2} (1 + x^{2})

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = coth (1 + x^{2})

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

\frac{d x}{d x} = 1

\frac{d}{d x} (coth (1 + x^{2})) = - csch^{2} (1 + x^{2}) \cdot 2 x

= 1 \cdot coth (1 + x^{2}) + (- csch^{2} (1 + x^{2}) \cdot 2 x) x

Vereinfache

1 \cdot coth (1 + x^{2}) + (- csch^{2} (1 + x^{2}) \cdot 2 x) x : coth (1 + x^{2}) - 2 x^{2} csch^{2} (1 + x^{2})

= coth (1 + x^{2}) - 2 x^{2} csch^{2} (1 + x^{2})

\frac{\partial}{\partial x} (sin (5 x - 8 y))

a re a e^{x}, e^{- 3 x}, x = ln (3)

\int \frac{9 x + 6}{( x - 6 ) ( x + 4 )} d x

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

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