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Popular >

derivative of f(x)=sqrt(x^2-x-2)

Solution

derivative of

f (x) = x^{2} - x - 2

Solution

\frac{2 x - 1}{2 x ^{2} - x - 2}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (6x^2+4x+4)/(sqrt(x))derivative of

\frac{6 x ^{2} + 4 x + 4}{x}

integral of (x^2+2x+1)^5(x+1)

\int (x^{2} + 2 x + 1)^{5} (x + 1) d x

integral from-1 to 4 of 4-x^2+3x

\int_{- 1}^{4} 4 - x^{2} + 3 x d x

integral of (1/3)x^3

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

limit as x approaches 1 of (x+1)/(x-1)

x \to 1 lim (\frac{x + 1}{x - 1})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x^2-x-2) ?
The derivative of f(x)=sqrt(x^2-x-2) is (2x-1)/(2sqrt(x^2-x-2))
What is the first derivative of f(x)=sqrt(x^2-x-2) ?
The first derivative of f(x)=sqrt(x^2-x-2) is (2x-1)/(2sqrt(x^2-x-2))