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Popular >

derivative of y=ln(3x^2+2x-1)

Solution

derivative of

y = ln (3 x^{2} + 2 x - 1)

Solution

\frac{6 x + 2}{3 x ^{2} + 2 x - 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} + 2 x - 1) = 6 x + 2

= \frac{1}{3 x ^{2} + 2 x - 1} (6 x + 2)

Simplify

\frac{1}{3 x ^{2} + 2 x - 1} (6 x + 2) : \frac{6 x + 2}{3 x ^{2} + 2 x - 1}

= \frac{6 x + 2}{3 x ^{2} + 2 x - 1}

Popular Examples

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\int \frac{8 e ^{4 x}}{x} d x

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y = \frac{2}{1 - x ^{2}}

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\frac{d}{d x} (sin (2 x) + cos (2 x))

limit as x approaches 3 of xsqrt(25-x^2)

x \to 3 lim (x 25 - x^{2})

(\partial)/(\partial x)(e^y)

\frac{\partial}{\partial x} (e^{y})

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(3x^2+2x-1) ?
The derivative of y=ln(3x^2+2x-1) is (6x+2)/(3x^2+2x-1)
What is the first derivative of y=ln(3x^2+2x-1) ?
The first derivative of y=ln(3x^2+2x-1) is (6x+2)/(3x^2+2x-1)