What is the derivative of (ce^x/(1+ce^x)) ?

The derivative of (ce^x/(1+ce^x)) is (ce^x)/((1+ce^x)^2)

What is the first derivative of (ce^x/(1+ce^x)) ?

The first derivative of (ce^x/(1+ce^x)) is (ce^x)/((1+ce^x)^2)

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Popular >

\frac{d}{d x} (\frac{c e ^{x}}{1 + c e ^{x}})

\frac{c e ^{x}}{( 1 + c e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{c e ^{x}}{1 + c e ^{x}})

Take the constant out:

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

= c \frac{d}{d x} (\frac{e ^{x}}{1 + c e ^{x}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (1 + c e^{x}) = c e^{x}

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

Simplify

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

= \frac{c e ^{x}}{( 1 + c e ^{x} ) ^{2}}

y = x^{2} + 7, (3, 16)

\frac{d}{d x} (x^{3} + 2 x + 1)

\int sin (3 x + 2) d x

y = 4 x cos (x), at x = π

\int \frac{1}{csc ^{2} ( x )} d x

What is the derivative of (ce^x/(1+ce^x)) ?
The derivative of (ce^x/(1+ce^x)) is (ce^x)/((1+ce^x)^2)
What is the first derivative of (ce^x/(1+ce^x)) ?
The first derivative of (ce^x/(1+ce^x)) is (ce^x)/((1+ce^x)^2)