What is the derivative of |x-1|+|2x+3| ?

The derivative of |x-1|+|2x+3| is (x-1)/(|x-1|)+(2(2x+3))/(|2x+3|)

What is the first derivative of |x-1|+|2x+3| ?

The first derivative of |x-1|+|2x+3| is (x-1)/(|x-1|)+(2(2x+3))/(|2x+3|)

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\frac{d}{d x} (∣ x - 1 ∣ + ∣ 2 x + 3 ∣)

\frac{x - 1}{∣ x - 1 ∣} + \frac{2 ( 2 x + 3 )}{∣ 2 x + 3 ∣}

Solution steps

\frac{d}{d x} (∣ x - 1 ∣ + ∣ 2 x + 3 ∣)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (∣ x - 1 ∣) + \frac{d}{d x} (∣ 2 x + 3 ∣)

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

\frac{d}{d x} (∣ 2 x + 3 ∣) = \frac{2 ( 2 x + 3 )}{∣ 2 x + 3 ∣}

= \frac{x - 1}{∣ x - 1 ∣} + \frac{2 ( 2 x + 3 )}{∣ 2 x + 3 ∣}

y = 2 x^{2}, y = 8 x - 6 x^{2}

\int_{0}^{4 π} x^{2} sin (2 x) d x

\int 5 - cos (x) d x

x \to \frac{π}{2} lim (sec^{2} (x))

What is the derivative of |x-1|+|2x+3| ?
The derivative of |x-1|+|2x+3| is (x-1)/(|x-1|)+(2(2x+3))/(|2x+3|)
What is the first derivative of |x-1|+|2x+3| ?
The first derivative of |x-1|+|2x+3| is (x-1)/(|x-1|)+(2(2x+3))/(|2x+3|)