What is the derivative of (3x)/(2e^x-e^{-x)} ?

The derivative of (3x)/(2e^x-e^{-x)} is (3(2e^x-e^{-x}-x(2e^x+e^{-x})))/((2e^x-e^{-x))^2}

What is the first derivative of (3x)/(2e^x-e^{-x)} ?

The first derivative of (3x)/(2e^x-e^{-x)} is (3(2e^x-e^{-x}-x(2e^x+e^{-x})))/((2e^x-e^{-x))^2}

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derivative of

\frac{3 x}{2 e ^{x} - e ^{- x}}

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

Solution steps

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

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x}{2 e ^{x} - e ^{- x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 3 \cdot \frac{\frac{d x}{d x} ( 2 e ^{x} - e ^{- x} ) - \frac{d}{d x} ( 2 e ^{x} - e ^{- x} ) x}{( 2 e ^{x} - e ^{- x} ) ^{2}}

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

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

= 3 \cdot \frac{1 \cdot ( 2 e ^{x} - e ^{- x} ) - ( 2 e ^{x} + e ^{- x} ) x}{( 2 e ^{x} - e ^{- x} ) ^{2}}

Simplify

3 \cdot \frac{1 \cdot ( 2 e ^{x} - e ^{- x} ) - ( 2 e ^{x} + e ^{- x} ) x}{( 2 e ^{x} - e ^{- x} ) ^{2}} : \frac{3 ( 2 e ^{x} - e ^{- x} - x ( 2 e ^{x} + e ^{- x} ) )}{( 2 e ^{x} - e ^{- x} ) ^{2}}

= \frac{3 ( 2 e ^{x} - e ^{- x} - x ( 2 e ^{x} + e ^{- x} ) )}{( 2 e ^{x} - e ^{- x} ) ^{2}}

x \to 2 lim (\frac{4}{( x - 2 ) ^{2}})

f (x) = 322560 (2 x + 5)

\frac{d y}{d x} = sin (5 x), y (0) = 2

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

n = 0 \sum \infty \frac{n !}{5 ^{n}}

What is the derivative of (3x)/(2e^x-e^{-x)} ?
The derivative of (3x)/(2e^x-e^{-x)} is (3(2e^x-e^{-x}-x(2e^x+e^{-x})))/((2e^x-e^{-x))^2}
What is the first derivative of (3x)/(2e^x-e^{-x)} ?
The first derivative of (3x)/(2e^x-e^{-x)} is (3(2e^x-e^{-x}-x(2e^x+e^{-x})))/((2e^x-e^{-x))^2}