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Popular Calculus >

derivative of sqrt(1+x+x^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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