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Popular >

derivative of sqrt(x^2-4x+5)

Solution

derivative of

x^{2} - 4 x + 5

Solution

\frac{x - 2}{x ^{2} - 4 x + 5}

Solution steps

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

Apply the chain rule:

\frac{1}{2 x ^{2} - 4 x + 5} \frac{d}{d x} (x^{2} - 4 x + 5)

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

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

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

Simplify

\frac{1}{2 x ^{2} - 4 x + 5} (2 x - 4) : \frac{x - 2}{x ^{2} - 4 x + 5}

= \frac{x - 2}{x ^{2} - 4 x + 5}

Popular Examples

integral from 3 to 7 of e^x

\int_{3}^{7} e^{x} d x

(\partial)/(\partial x)(ln(4x^2+3y^2+6))

\frac{\partial}{\partial x} (ln (4 x^{2} + 3 y^{2} + 6))

sum from n=0 to infinity of 1/(8^n)

n = 0 \sum \infty \frac{1}{8 ^{n}}

integral of (3+x)/(3-x)

\int \frac{3 + x}{3 - x} d x

derivative of 3/2 x^{1/2}

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

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2-4x+5) ?
The derivative of sqrt(x^2-4x+5) is (x-2)/(sqrt(x^2-4x+5))
What is the first derivative of sqrt(x^2-4x+5) ?
The first derivative of sqrt(x^2-4x+5) is (x-2)/(sqrt(x^2-4x+5))