What is the derivative of xcoth(1+x^2) ?

The derivative of xcoth(1+x^2) is coth(1+x^2)-2x^2csch^2(1+x^2)

What is the first derivative of xcoth(1+x^2) ?

The first derivative of xcoth(1+x^2) is coth(1+x^2)-2x^2csch^2(1+x^2)

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

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

Solution steps

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

Apply the Product Rule:

(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

Simplify

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})

y = ln (1 + e^{x})

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

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

What is the derivative of xcoth(1+x^2) ?
The derivative of xcoth(1+x^2) is coth(1+x^2)-2x^2csch^2(1+x^2)
What is the first derivative of xcoth(1+x^2) ?
The first derivative of xcoth(1+x^2) is coth(1+x^2)-2x^2csch^2(1+x^2)