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

The derivative of (x^2+1/(x+e^x+2)) is (x^2-e^xx^2+2e^xx+4x-e^x-1)/((x+e^x+2)^2)

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

The first derivative of (x^2+1/(x+e^x+2)) is (x^2-e^xx^2+2e^xx+4x-e^x-1)/((x+e^x+2)^2)

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

\frac{x ^{2} - e ^{x} x ^{2} + 2 e ^{x} x + 4 x - e ^{x} - 1}{( x + e ^{x} + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 x (x + e^{x} + 2) - (e^{x} + 1) (x^{2} + 1) : x^{2} - e^{x} x^{2} + 2 e^{x} x + 4 x - e^{x} - 1

= \frac{x ^{2} - e ^{x} x ^{2} + 2 e ^{x} x + 4 x - e ^{x} - 1}{( x + e ^{x} + 2 ) ^{2}}

\int \frac{x ^{6}}{( 1 + x ^{2} ) ^{2}} d x

(1 - y^{2}) d x - x y d y = 0

\int (x^{2} + 1)^{2} 2 x d x

y^{^{'}} = \frac{t}{y e ^{- y^{2}} + y e ^{- y^{2}} t ^{2}}

\frac{d}{d x} (- \frac{14}{x ^{4}})

What is the derivative of (x^2+1/(x+e^x+2)) ?
The derivative of (x^2+1/(x+e^x+2)) is (x^2-e^xx^2+2e^xx+4x-e^x-1)/((x+e^x+2)^2)
What is the first derivative of (x^2+1/(x+e^x+2)) ?
The first derivative of (x^2+1/(x+e^x+2)) is (x^2-e^xx^2+2e^xx+4x-e^x-1)/((x+e^x+2)^2)