What is the derivative of (1400/((1+6e^{-0.02x))}) ?

The derivative of (1400/((1+6e^{-0.02x))}) is (168e^{-0.02x})/((1+6e^{-0.02x))^2}

What is the first derivative of (1400/((1+6e^{-0.02x))}) ?

The first derivative of (1400/((1+6e^{-0.02x))}) is (168e^{-0.02x})/((1+6e^{-0.02x))^2}

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\frac{d}{d x} (\frac{1400}{( 1 + 6 e ^{- 0.02 x} )})

\frac{168 e ^{- 0.02 x}}{( 1 + 6 e ^{- 0.02 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1400}{( 1 + 6 e ^{- 0.02 x} )})

Take the constant out:

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

= 1400 \frac{d}{d x} (\frac{1}{1 + 6 e ^{- 0.02 x}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 1400 \frac{d}{d x} ((1 + 6 e^{- 0.02 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 6 e ^{- 0.02 x} ) ^{2}} \frac{d}{d x} (1 + 6 e^{- 0.02 x})

= - \frac{1}{( 1 + 6 e ^{- 0.02 x} ) ^{2}} \frac{d}{d x} (1 + 6 e^{- 0.02 x})

\frac{d}{d x} (1 + 6 e^{- 0.02 x}) = - 0.12 e^{- 0.02 x}

= 1400 (- \frac{1}{( 1 + 6 e ^{- 0.02 x} ) ^{2}} (- 0.12 e^{- 0.02 x}))

Simplify

1400 (- \frac{1}{( 1 + 6 e ^{- 0.02 x} ) ^{2}} (- 0.12 e^{- 0.02 x})) : \frac{168 e ^{- 0.02 x}}{( 1 + 6 e ^{- 0.02 x} ) ^{2}}

= \frac{168 e ^{- 0.02 x}}{( 1 + 6 e ^{- 0.02 x} ) ^{2}}

What is the derivative of (1400/((1+6e^{-0.02x))}) ?
The derivative of (1400/((1+6e^{-0.02x))}) is (168e^{-0.02x})/((1+6e^{-0.02x))^2}
What is the first derivative of (1400/((1+6e^{-0.02x))}) ?
The first derivative of (1400/((1+6e^{-0.02x))}) is (168e^{-0.02x})/((1+6e^{-0.02x))^2}