What is the derivative of ln(8x^2+7x+2) ?

The derivative of ln(8x^2+7x+2) is (16x+7)/(8x^2+7x+2)

What is the first derivative of ln(8x^2+7x+2) ?

The first derivative of ln(8x^2+7x+2) is (16x+7)/(8x^2+7x+2)

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\frac{d}{d x} (ln (8 x^{2} + 7 x + 2))

\frac{16 x + 7}{8 x ^{2} + 7 x + 2}

Solution steps

\frac{d}{d x} (ln (8 x^{2} + 7 x + 2))

Apply the chain rule:

\frac{1}{8 x ^{2} + 7 x + 2} \frac{d}{d x} (8 x^{2} + 7 x + 2)

= \frac{1}{8 x ^{2} + 7 x + 2} \frac{d}{d x} (8 x^{2} + 7 x + 2)

\frac{d}{d x} (8 x^{2} + 7 x + 2) = 16 x + 7

= \frac{1}{8 x ^{2} + 7 x + 2} (16 x + 7)

Simplify

\frac{1}{8 x ^{2} + 7 x + 2} (16 x + 7) : \frac{16 x + 7}{8 x ^{2} + 7 x + 2}

= \frac{16 x + 7}{8 x ^{2} + 7 x + 2}

What is the derivative of ln(8x^2+7x+2) ?
The derivative of ln(8x^2+7x+2) is (16x+7)/(8x^2+7x+2)
What is the first derivative of ln(8x^2+7x+2) ?
The first derivative of ln(8x^2+7x+2) is (16x+7)/(8x^2+7x+2)