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Popular >

derivative of ln(sqrt(3x^5+2))

Solution

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

Solution

\frac{15 x ^{4}}{2 ( 3 x ^{5} + 2 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{5} + 2) = \frac{15 x ^{4}}{2 3 x ^{5} + 2}

= \frac{1}{3 x ^{5} + 2} \cdot \frac{15 x ^{4}}{2 3 x ^{5} + 2}

Simplify

\frac{1}{3 x ^{5} + 2} \cdot \frac{15 x ^{4}}{2 3 x ^{5} + 2} : \frac{15 x ^{4}}{2 ( 3 x ^{5} + 2 )}

= \frac{15 x ^{4}}{2 ( 3 x ^{5} + 2 )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(sqrt(3x^5+2)) ?
The derivative of ln(sqrt(3x^5+2)) is (15x^4)/(2(3x^5+2))
What is the first derivative of ln(sqrt(3x^5+2)) ?
The first derivative of ln(sqrt(3x^5+2)) is (15x^4)/(2(3x^5+2))