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))

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derivative of

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

\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}

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))