What is the derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) ?

The derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) is 0.55555…(-2.8e^{-2.8x}+4.6e^{-4.6x})

What is the first derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) ?

The first derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) is 0.55555…(-2.8e^{-2.8x}+4.6e^{-4.6x})

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\frac{d}{d x} (\frac{e ^{- 2.8 x} - e ^{- 4.6 x}}{1.8})

0.55555 \dots (- 2.8 e^{- 2.8 x} + 4.6 e^{- 4.6 x})

Solution steps

\frac{d}{d x} (\frac{e ^{- 2.8 x} - e ^{- 4.6 x}}{1.8})

Take the constant out:

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

= \frac{1}{1.8} \frac{d}{d x} (e^{- 2.8 x} - e^{- 4.6 x})

Apply the Sum/Difference Rule:

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

= \frac{1}{1.8} (\frac{d}{d x} (e^{- 2.8 x}) - \frac{d}{d x} (e^{- 4.6 x}))

\frac{d}{d x} (e^{- 2.8 x}) = - 2.8 e^{- 2.8 x}

\frac{d}{d x} (e^{- 4.6 x}) = - 4.6 e^{- 4.6 x}

= \frac{1}{1.8} (- 2.8 e^{- 2.8 x} - (- 4.6 e^{- 4.6 x}))

Simplify

= 0.55555 \dots (- 2.8 e^{- 2.8 x} + 4.6 e^{- 4.6 x})

What is the derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) ?
The derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) is 0.55555…(-2.8e^{-2.8x}+4.6e^{-4.6x})
What is the first derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) ?
The first derivative of (e^{-2.8x}-e^{-4.6x}/(1.8)) is 0.55555…(-2.8e^{-2.8x}+4.6e^{-4.6x})