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Popular >

derivative of ln(x^4+x)

Solution

derivative of

ln (x^{4} + x)

Solution

\frac{4 x ^{3} + 1}{x ^{4} + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{x ^{4} + x} (4 x^{3} + 1) : \frac{4 x ^{3} + 1}{x ^{4} + x}

= \frac{4 x ^{3} + 1}{x ^{4} + x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x^4+x) ?
The derivative of ln(x^4+x) is (4x^3+1)/(x^4+x)
What is the first derivative of ln(x^4+x) ?
The first derivative of ln(x^4+x) is (4x^3+1)/(x^4+x)