What is the derivative of ln(4x^3+5x^2+2x+5) ?

The derivative of ln(4x^3+5x^2+2x+5) is (12x^2+10x+2)/(4x^3+5x^2+2x+5)

What is the first derivative of ln(4x^3+5x^2+2x+5) ?

The first derivative of ln(4x^3+5x^2+2x+5) is (12x^2+10x+2)/(4x^3+5x^2+2x+5)

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derivative of

ln (4 x^{3} + 5 x^{2} + 2 x + 5)

\frac{12 x ^{2} + 10 x + 2}{4 x ^{3} + 5 x ^{2} + 2 x + 5}

Solution steps

\frac{d}{d x} (ln (4 x^{3} + 5 x^{2} + 2 x + 5))

Apply the chain rule:

\frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} \frac{d}{d x} (4 x^{3} + 5 x^{2} + 2 x + 5)

= \frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} \frac{d}{d x} (4 x^{3} + 5 x^{2} + 2 x + 5)

\frac{d}{d x} (4 x^{3} + 5 x^{2} + 2 x + 5) = 12 x^{2} + 10 x + 2

= \frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} (12 x^{2} + 10 x + 2)

Simplify

\frac{1}{4 x ^{3} + 5 x ^{2} + 2 x + 5} (12 x^{2} + 10 x + 2) : \frac{12 x ^{2} + 10 x + 2}{4 x ^{3} + 5 x ^{2} + 2 x + 5}

= \frac{12 x ^{2} + 10 x + 2}{4 x ^{3} + 5 x ^{2} + 2 x + 5}

What is the derivative of ln(4x^3+5x^2+2x+5) ?
The derivative of ln(4x^3+5x^2+2x+5) is (12x^2+10x+2)/(4x^3+5x^2+2x+5)
What is the first derivative of ln(4x^3+5x^2+2x+5) ?
The first derivative of ln(4x^3+5x^2+2x+5) is (12x^2+10x+2)/(4x^3+5x^2+2x+5)