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Popular >

derivative of log_{e}(x^2+x+1)

Solution

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

Solution

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

Solution steps

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

Simplify

lo g_{e} (x^{2} + x + 1) : ln (x^{2} + x + 1)

= \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}

Popular Examples

derivative of (-3x^5-3^3)

\frac{d}{d x} ((- 3 x^{5} - 3)^{3})

integral of x(1-x)^{2/3}

\int x (1 - x)^{\frac{2}{3}} d x

limit as x approaches 0+of 2x^{3x}

x \to 0 + lim (2 x^{3 x})

derivative of 1/(x^3+4x^2)

\frac{d}{d x} (\frac{1}{x ^{3} + 4 x ^{2}})

derivative of x^2cos(x-2xsin(x)-2cos(x))

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

Frequently Asked Questions (FAQ)

What is the derivative of log_{e}(x^2+x+1) ?
The derivative of log_{e}(x^2+x+1) is (2x+1)/(x^2+x+1)
What is the first derivative of log_{e}(x^2+x+1) ?
The first derivative of log_{e}(x^2+x+1) is (2x+1)/(x^2+x+1)