What is the derivative of (3e^x)/((3+e^x)^2) ?

The derivative of (3e^x)/((3+e^x)^2) is (3e^x(-e^x+3))/((3+e^x)^3)

What is the first derivative of (3e^x)/((3+e^x)^2) ?

The first derivative of (3e^x)/((3+e^x)^2) is (3e^x(-e^x+3))/((3+e^x)^3)

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derivative of

\frac{3 e ^{x}}{( 3 + e ^{x} ) ^{2}}

\frac{3 e ^{x} ( - e ^{x} + 3 )}{( 3 + e ^{x} ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d}{d x} ( e ^{x} ) ( 3 + e ^{x} ) ^{2} - \frac{d}{d x} ( ( 3 + e ^{x} ) ^{2} ) e ^{x}}{( ( 3 + e ^{x} ) ^{2} ) ^{2}}

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

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

= 3 \cdot \frac{e ^{x} ( 3 + e ^{x} ) ^{2} - 2 ( 3 + e ^{x} ) e ^{x} e ^{x}}{( ( 3 + e ^{x} ) ^{2} ) ^{2}}

Simplify

3 \cdot \frac{e ^{x} ( 3 + e ^{x} ) ^{2} - 2 ( 3 + e ^{x} ) e ^{x} e ^{x}}{( ( 3 + e ^{x} ) ^{2} ) ^{2}} : \frac{3 e ^{x} ( - e ^{x} + 3 )}{( 3 + e ^{x} ) ^{3}}

= \frac{3 e ^{x} ( - e ^{x} + 3 )}{( 3 + e ^{x} ) ^{3}}

\frac{\partial}{\partial y} (5 + x^{2} + y^{2} + 2 x y)

y^{^{''}} + 12 y^{^{'}} + 36 y = 0

\int \frac{( ( ln ( x ) ) ^{7} )}{x} d x

\frac{d}{d x} (- (x + 1)^{- 1})

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

What is the derivative of (3e^x)/((3+e^x)^2) ?
The derivative of (3e^x)/((3+e^x)^2) is (3e^x(-e^x+3))/((3+e^x)^3)
What is the first derivative of (3e^x)/((3+e^x)^2) ?
The first derivative of (3e^x)/((3+e^x)^2) is (3e^x(-e^x+3))/((3+e^x)^3)