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Popular >

derivative of 2sinh(x/5)

Solution

\frac{d}{d x} (2 sinh (\frac{x}{5}))

Solution

\frac{2}{5} cosh (\frac{x}{5})

Solution steps

\frac{d}{d x} (2 sinh (\frac{x}{5}))

Take the constant out:

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

= 2 \frac{d}{d x} (sinh (\frac{x}{5}))

Apply the chain rule:

cosh (\frac{x}{5}) \frac{d}{d x} (\frac{x}{5})

= cosh (\frac{x}{5}) \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= 2 cosh (\frac{x}{5}) \frac{1}{5}

Simplify

2 cosh (\frac{x}{5}) \frac{1}{5} : \frac{2}{5} cosh (\frac{x}{5})

= \frac{2}{5} cosh (\frac{x}{5})

Popular Examples

limit as x approaches 1 of x/(x^2-1)

x \to 1 lim (\frac{x}{x ^{2} - 1})

derivative of (5x-2x^4^3)

\frac{d}{d x} ((5 x - 2 x^{4})^{3})

integral of 1/((x+2)sqrt(x^2+4x))

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

limit as x approaches 5+of sqrt(25-x^2)

x \to 5 + lim (25 - x^{2})

integral of 1/(sqrt(36+x^2))

\int \frac{1}{36 + x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of 2sinh(x/5) ?
The derivative of 2sinh(x/5) is 2/5 cosh(x/5)
What is the first derivative of 2sinh(x/5) ?
The first derivative of 2sinh(x/5) is 2/5 cosh(x/5)