What is the derivative of (e^x+1/(e^x+2)) ?

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

x \to 2 lim (\frac{x ^{3} - 8}{x - 2})

\frac{d}{d t} (e^{2 t} cos (t))

y = \frac{ln ( 9 x )}{9 x}

\int_{- 1}^{7} (4 x + 7) - (x^{2} - 2 x) d x

\int 8 t d t

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