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Popular >

derivative of |x-1|^3

Solution

\frac{d}{d x} (∣ x - 1 ∣^{3})

Solution

\frac{3 ( x - 1 ) ^{3}}{∣ x - 1 ∣}

Solution steps

\frac{d}{d x} (∣ x - 1 ∣^{3})

Apply the chain rule:

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

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

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

= 3 ∣ x - 1 ∣^{2} \frac{x - 1}{∣ x - 1 ∣}

Simplify

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

= \frac{3 ( x - 1 ) ^{3}}{∣ x - 1 ∣}

Popular Examples

limit as x approaches 0 of |x-1|

x \to 0 lim (∣ x - 1 ∣)

limit as x approaches 5 of 2xsqrt(5)

x \to 5 lim (2 x 5)

(\partial)/(\partial x)(e^{2x}*2)

\frac{\partial}{\partial x} (e^{2 x} \cdot 2)

derivative of f(x)=(2x-7)^4(x^2+x+1)^5 derivative of

f (x) = (2 x - 7)^{4} (x^{2} + x + 1)^{5}

integral of (1+x^2)/(x^3)

\int \frac{1 + x ^{2}}{x ^{3}} d x

Frequently Asked Questions (FAQ)

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