What is the derivative of sinh^3(1/x) ?

The derivative of sinh^3(1/x) is -(3sinh^2(1/x)cosh(1/x))/(x^2)

What is the first derivative of sinh^3(1/x) ?

The first derivative of sinh^3(1/x) is -(3sinh^2(1/x)cosh(1/x))/(x^2)

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\frac{d}{d x} (sinh^{3} (\frac{1}{x}))

- \frac{3 sinh ^{2} ( \frac{1}{x} ) cosh ( \frac{1}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (sinh^{3} (\frac{1}{x}))

Apply the chain rule:

3 (sinh (\frac{1}{x}))^{2} \frac{d}{d x} (sinh (\frac{1}{x}))

= 3 (sinh (\frac{1}{x}))^{2} \frac{d}{d x} (sinh (\frac{1}{x}))

\frac{d}{d x} (sinh (\frac{1}{x})) = - \frac{cosh ( \frac{1}{x} )}{x ^{2}}

= 3 (sinh (\frac{1}{x}))^{2} (- \frac{cosh ( \frac{1}{x} )}{x ^{2}})

Simplify

3 sinh^{2} (\frac{1}{x}) (- \frac{cosh ( \frac{1}{x} )}{x ^{2}}) : - \frac{3 sinh ^{2} ( \frac{1}{x} ) cosh ( \frac{1}{x} )}{x ^{2}}

= - \frac{3 sinh ^{2} ( \frac{1}{x} ) cosh ( \frac{1}{x} )}{x ^{2}}

\int (sin (x) - 6 cos (x)) d x

\int_{1}^{\infty} \frac{2}{x} d x

\int \frac{y ^{2} + 1}{y} d y

\frac{d}{d x} ((x^{2} - 3 x + 4)^{4})

\frac{1}{1 - e ^{x}}

What is the derivative of sinh^3(1/x) ?
The derivative of sinh^3(1/x) is -(3sinh^2(1/x)cosh(1/x))/(x^2)
What is the first derivative of sinh^3(1/x) ?
The first derivative of sinh^3(1/x) is -(3sinh^2(1/x)cosh(1/x))/(x^2)