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Popular >

derivative of ln(5x^4+4x)

Solution

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

Solution

\frac{20 x ^{3} + 4}{5 x ^{4} + 4 x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{4} + 4 x) = 20 x^{3} + 4

= \frac{1}{5 x ^{4} + 4 x} (20 x^{3} + 4)

Simplify

\frac{1}{5 x ^{4} + 4 x} (20 x^{3} + 4) : \frac{20 x ^{3} + 4}{5 x ^{4} + 4 x}

= \frac{20 x ^{3} + 4}{5 x ^{4} + 4 x}

Graph

Popular Examples

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\int \frac{6 x ^{2} + 5 x + 6}{( x ^{2} + 1 ) ^{2}} d x

y^'=(3^2y^2+1)/3 ,y(0)=-0.5

y^{^{'}} = \frac{3 ^{2} y ^{2} + 1}{3}, y (0) = - 0.5

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\int_{0}^{5} π (25 - y^{2}) d y

(\partial)/(\partial x)(ln(x+3y+5z))

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integral from 1/2 to 3 of 12xln(2x)

\int_{\frac{1}{2}}^{3} 12 x ln (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(5x^4+4x) ?
The derivative of ln(5x^4+4x) is (20x^3+4)/(5x^4+4x)
What is the first derivative of ln(5x^4+4x) ?
The first derivative of ln(5x^4+4x) is (20x^3+4)/(5x^4+4x)