What is the derivative of xcoth(6+x^2) ?

The derivative of xcoth(6+x^2) is coth(6+x^2)-2x^2csch^2(6+x^2)

What is the first derivative of xcoth(6+x^2) ?

The first derivative of xcoth(6+x^2) is coth(6+x^2)-2x^2csch^2(6+x^2)

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\frac{d}{d x} (x coth (6 + x^{2}))

coth (6 + x^{2}) - 2 x^{2} csch^{2} (6 + x^{2})

Solution steps

\frac{d}{d x} (x coth (6 + x^{2}))

Apply the Product Rule:

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

f = x, g = coth (6 + x^{2})

= \frac{d x}{d x} coth (6 + x^{2}) + \frac{d}{d x} (coth (6 + x^{2})) x

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

\frac{d}{d x} (coth (6 + x^{2})) = - csch^{2} (6 + x^{2}) \cdot 2 x

= 1 \cdot coth (6 + x^{2}) + (- csch^{2} (6 + x^{2}) \cdot 2 x) x

Simplify

1 \cdot coth (6 + x^{2}) + (- csch^{2} (6 + x^{2}) \cdot 2 x) x : coth (6 + x^{2}) - 2 x^{2} csch^{2} (6 + x^{2})

= coth (6 + x^{2}) - 2 x^{2} csch^{2} (6 + x^{2})

\int \frac{e ^{x}}{( x - 1 )} d x

y^{^{'}} = - \frac{π}{2} t (1 + y^{2})

\frac{d}{d x} (\frac{ln ( x + 1 )}{x + 1})

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

What is the derivative of xcoth(6+x^2) ?
The derivative of xcoth(6+x^2) is coth(6+x^2)-2x^2csch^2(6+x^2)
What is the first derivative of xcoth(6+x^2) ?
The first derivative of xcoth(6+x^2) is coth(6+x^2)-2x^2csch^2(6+x^2)