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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

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

Graph

Popular Examples

implicit 3x^3+2y^3=12 implicit derivative

3 x^{3} + 2 y^{3} = 12

(dy)/(dx)=(x+6)/(x+1)

\frac{d y}{d x} = \frac{x + 6}{x + 1}

integral of (1+x^6)/(x^2)

\int \frac{1 + x ^{6}}{x ^{2}} d x

integral of cosh(x)+5/(sin(x))

\int cosh (x) + \frac{5}{sin ( x )} d x

y^{''}+16y=0,y(0)=2,y^'(0)=0

y^{^{''}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

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