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Popular >

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

Solution

derivative of

f (x) = x^{2} + x + 1

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

y^{'''}-6y^{''}+8y^'=0

y^{^{'''}} - 6 y^{^{''}} + 8 y^{^{'}} = 0

integral of 1/(p-p^2)

\int \frac{1}{p - p ^{2}} d p

sum from n=0 to infinity}2^{-n of+3^{-n}

n = 0 \sum \infty 2^{- n} + 3^{- n}

derivative of 1/((x+1))

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

derivative of arccsc(-x^2)

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

Frequently Asked Questions (FAQ)

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