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Popular >

derivative of ln(9x^2-7x+1)

Solution

\frac{d}{d x} (ln (9 x^{2} - 7 x + 1))

Solution

\frac{18 x - 7}{9 x ^{2} - 7 x + 1}

Solution steps

\frac{d}{d x} (ln (9 x^{2} - 7 x + 1))

Apply the chain rule:

\frac{1}{9 x ^{2} - 7 x + 1} \frac{d}{d x} (9 x^{2} - 7 x + 1)

= \frac{1}{9 x ^{2} - 7 x + 1} \frac{d}{d x} (9 x^{2} - 7 x + 1)

\frac{d}{d x} (9 x^{2} - 7 x + 1) = 18 x - 7

= \frac{1}{9 x ^{2} - 7 x + 1} (18 x - 7)

Simplify

\frac{1}{9 x ^{2} - 7 x + 1} (18 x - 7) : \frac{18 x - 7}{9 x ^{2} - 7 x + 1}

= \frac{18 x - 7}{9 x ^{2} - 7 x + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(9x^2-7x+1) ?
The derivative of ln(9x^2-7x+1) is (18x-7)/(9x^2-7x+1)
What is the first derivative of ln(9x^2-7x+1) ?
The first derivative of ln(9x^2-7x+1) is (18x-7)/(9x^2-7x+1)