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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\int \frac{( x + 4 )}{x ^{2} + 2 x + 5} d x

\frac{s}{( s ^{2} + 25 ) ( s - 1 )}

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

\frac{( x + x ) d y}{d x} = y + y

x \to 6 + lim (\frac{x}{x - 6})

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