What is the derivative of 1/(|x|+1)+1/(|x-2|+1) ?

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

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

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

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derivative of

\frac{1}{∣ x ∣ + 1} + \frac{1}{∣ x - 2 ∣ + 1}

\frac{- 4 x ^{3} - x ^{3} ∣ x ∣ + 12 x ^{2} + 2 x ^{2} ∣ x ∣ - x ∣ x - 2 ∣ ^{3} - 8 x - x ∣ x - 2 ∣ - x ∣ x ∣ + 2 ∣ x ∣}{∣ x ∣ ∣ x - 2 ∣ ( ∣ x ∣ + 1 ) ^{2} ( ∣ x - 2 ∣ + 1 ) ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

- \frac{x}{∣ x ∣ ( ∣ x ∣ + 1 ) ^{2}} - \frac{x - 2}{∣ x - 2 ∣ ( ∣ x - 2 ∣ + 1 ) ^{2}} : \frac{- 4 x ^{3} - x ^{3} ∣ x ∣ + 12 x ^{2} + 2 x ^{2} ∣ x ∣ - x ∣ x - 2 ∣ ^{3} - 8 x - x ∣ x - 2 ∣ - x ∣ x ∣ + 2 ∣ x ∣}{∣ x ∣ ∣ x - 2 ∣ ( ∣ x ∣ + 1 ) ^{2} ( ∣ x - 2 ∣ + 1 ) ^{2}}

= \frac{- 4 x ^{3} - x ^{3} ∣ x ∣ + 12 x ^{2} + 2 x ^{2} ∣ x ∣ - x ∣ x - 2 ∣ ^{3} - 8 x - x ∣ x - 2 ∣ - x ∣ x ∣ + 2 ∣ x ∣}{∣ x ∣ ∣ x - 2 ∣ ( ∣ x ∣ + 1 ) ^{2} ( ∣ x - 2 ∣ + 1 ) ^{2}}

\frac{d}{d x} (\frac{4374}{x ^{2}})

\frac{\partial}{\partial x} (5 e^{x y + 7})

\int \frac{x ^{5}}{1 + x ^{3}} d x

\frac{\partial}{\partial y} (\frac{y}{( x + y + z )})

\int_{- 2}^{3} \frac{31}{x ^{4}} d x

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