What is the derivative of e^{2x}-e^{-2x}-4x ?

The derivative of e^{2x}-e^{-2x}-4x is 2e^{2x}+2e^{-2x}-4

What is the first derivative of e^{2x}-e^{-2x}-4x ?

The first derivative of e^{2x}-e^{-2x}-4x is 2e^{2x}+2e^{-2x}-4

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

2 e^{2 x} + 2 e^{- 2 x} - 4

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{2 x}) - \frac{d}{d x} (e^{- 2 x}) - \frac{d}{d x} (4 x)

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

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

\frac{d}{d x} (4 x) = 4

= e^{2 x} \cdot 2 - (- 2 e^{- 2 x}) - 4

Simplify

= 2 e^{2 x} + 2 e^{- 2 x} - 4

What is the derivative of e^{2x}-e^{-2x}-4x ?
The derivative of e^{2x}-e^{-2x}-4x is 2e^{2x}+2e^{-2x}-4
What is the first derivative of e^{2x}-e^{-2x}-4x ?
The first derivative of e^{2x}-e^{-2x}-4x is 2e^{2x}+2e^{-2x}-4