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Popular >

derivative of x/(csch(x))

Solution

\frac{d}{d x} (\frac{x}{csch ( x )})

Solution

sinh (x) + x cosh (x)

Solution steps

\frac{d}{d x} (\frac{x}{csch ( x )})

Simplify

\frac{x}{csch ( x )} : x sinh (x)

= \frac{d}{d x} (x sinh (x))

Apply the Product Rule:

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

f = x, g = sinh (x)

= \frac{d x}{d x} sinh (x) + \frac{d}{d x} (sinh (x)) x

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

\frac{d}{d x} (sinh (x)) = cosh (x)

= 1 \cdot sinh (x) + cosh (x) x

Simplify

= sinh (x) + x cosh (x)

Popular Examples

integral of 30x*(x+1)^4

\int 30 x \cdot (x + 1)^{4} d x

derivative of (2x/((1+x^2)^2))

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

integral of (x^4)/(x^4-16)

\int \frac{x ^{4}}{x ^{4} - 16} d x

y^{''}+9y=2cos(3x)+3sin(3x)

y^{^{''}} + 9 y = 2 cos (3 x) + 3 sin (3 x)

tangent of f(x)=4sin(x),\at x= pi/2 tangent of

f (x) = 4 sin (x), at x = \frac{π}{2}

Frequently Asked Questions (FAQ)

What is the derivative of x/(csch(x)) ?
The derivative of x/(csch(x)) is sinh(x)+xcosh(x)
What is the first derivative of x/(csch(x)) ?
The first derivative of x/(csch(x)) is sinh(x)+xcosh(x)