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Popular >

derivative of 1-|1-x|

Solution

\frac{d}{d x} (1 - ∣ 1 - x ∣)

Solution

\frac{- x + 1}{∣ - x + 1 ∣}

Solution steps

\frac{d}{d x} (1 - ∣ 1 - x ∣)

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - (- \frac{1 - x}{∣ 1 - x ∣})

Simplify

= \frac{- x + 1}{∣ - x + 1 ∣}

Popular Examples

integral of (x^4)/x

\int \frac{x ^{4}}{x} d x

(x^2+2)^2y=(5x(y^2+1)^2)/((x^2+2)y^')-(x^4+4x^2+4)y

(x^{2} + 2)^{2} y = \frac{5 x ( y ^{2} + 1 ) ^{2}}{( x ^{2} + 2 ) y ^{^{'}}} - (x^{4} + 4 x^{2} + 4) y

(dy)/(dx)= 1/(x^4+4x^2)

\frac{d y}{d x} = \frac{1}{x ^{4} + 4 x ^{2}}

limit as x approaches 2 of sin(1/(x-2))

x \to 2 lim (sin (\frac{1}{x - 2}))

limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4))

x \to \infty lim (\frac{4 x ^{2} + 5 x}{10 + x ^{4}})

Frequently Asked Questions (FAQ)

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