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Popular >

derivative of ln(x^3+5x+3)

Solution

derivative of

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

Solution

\frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

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Frequently Asked Questions (FAQ)

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