What is the derivative of (90/(6+9e^{-0.025x)}) ?

The derivative of (90/(6+9e^{-0.025x)}) is (20.25e^{-0.025x})/((6+9e^{-0.025x))^2}

What is the first derivative of (90/(6+9e^{-0.025x)}) ?

The first derivative of (90/(6+9e^{-0.025x)}) is (20.25e^{-0.025x})/((6+9e^{-0.025x))^2}

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\frac{d}{d x} (\frac{90}{6 + 9 e ^{- 0.025 x}})

\frac{20.25 e ^{- 0.025 x}}{( 6 + 9 e ^{- 0.025 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{90}{6 + 9 e ^{- 0.025 x}})

Take the constant out:

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

= 90 \frac{d}{d x} (\frac{1}{6 + 9 e ^{- 0.025 x}})

Apply exponent rule:

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

= 90 \frac{d}{d x} ((6 + 9 e^{- 0.025 x})^{- 1})

Apply the chain rule:

- \frac{1}{( 6 + 9 e ^{- 0.025 x} ) ^{2}} \frac{d}{d x} (6 + 9 e^{- 0.025 x})

= - \frac{1}{( 6 + 9 e ^{- 0.025 x} ) ^{2}} \frac{d}{d x} (6 + 9 e^{- 0.025 x})

\frac{d}{d x} (6 + 9 e^{- 0.025 x}) = - 0.225 e^{- 0.025 x}

= 90 (- \frac{1}{( 6 + 9 e ^{- 0.025 x} ) ^{2}} (- 0.225 e^{- 0.025 x}))

Simplify

90 (- \frac{1}{( 6 + 9 e ^{- 0.025 x} ) ^{2}} (- 0.225 e^{- 0.025 x})) : \frac{20.25 e ^{- 0.025 x}}{( 6 + 9 e ^{- 0.025 x} ) ^{2}}

= \frac{20.25 e ^{- 0.025 x}}{( 6 + 9 e ^{- 0.025 x} ) ^{2}}

\frac{d y}{d t} = \frac{1 - t y ^{2}}{2 t ^{2} y}

\int 2 cos (t) d t

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

\int \frac{( 7 - x )}{x ^{2} - 4 x + 4} d x

y = 3 x + 6 cos (x), (0, 6)

What is the derivative of (90/(6+9e^{-0.025x)}) ?
The derivative of (90/(6+9e^{-0.025x)}) is (20.25e^{-0.025x})/((6+9e^{-0.025x))^2}
What is the first derivative of (90/(6+9e^{-0.025x)}) ?
The first derivative of (90/(6+9e^{-0.025x)}) is (20.25e^{-0.025x})/((6+9e^{-0.025x))^2}