What is the derivative of a*sinh(x/a) ?

The derivative of a*sinh(x/a) is cosh(x/a)

What is the first derivative of a*sinh(x/a) ?

The first derivative of a*sinh(x/a) is cosh(x/a)

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\frac{d}{d x} (a \cdot sinh (\frac{x}{a}))

cosh (\frac{x}{a})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

cosh (\frac{x}{a}) \frac{d}{d x} (\frac{x}{a})

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

\frac{d}{d x} (\frac{x}{a}) = \frac{1}{a}

= a cosh (\frac{x}{a}) \frac{1}{a}

Simplify

a cosh (\frac{x}{a}) \frac{1}{a} : cosh (\frac{x}{a})

= cosh (\frac{x}{a})

\int \frac{1}{4 x ^{2} + 16} d x

\frac{d}{d t} (t cos (2 t))

4 x + \frac{1}{x}

x sin (x^{2}) y^{^{'}} + y (4 x^{2} cos (x^{2}) - sin (x^{2})) = 0

\int x^{2} + 25 d x

What is the derivative of a*sinh(x/a) ?
The derivative of a*sinh(x/a) is cosh(x/a)
What is the first derivative of a*sinh(x/a) ?
The first derivative of a*sinh(x/a) is cosh(x/a)