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Popular >

derivative of ln(2x-sqrt(x))

Solution

\frac{d}{d x} (ln (2 x - x))

Solution

\frac{4 x - 1}{2 x ( 2 x - x )}

Solution steps

\frac{d}{d x} (ln (2 x - x))

Apply the chain rule:

\frac{1}{2 x - x} \frac{d}{d x} (2 x - x)

= \frac{1}{2 x - x} \frac{d}{d x} (2 x - x)

\frac{d}{d x} (2 x - x) = 2 - \frac{1}{2 x}

= \frac{1}{2 x - x} (2 - \frac{1}{2 x})

Simplify

\frac{1}{2 x - x} (2 - \frac{1}{2 x}) : \frac{4 x - 1}{2 x ( 2 x - x )}

= \frac{4 x - 1}{2 x ( 2 x - x )}

Popular Examples

integral of sqrt(x^3+x^2)(3x^2+2x)

\int x^{3} + x^{2} (3 x^{2} + 2 x) d x

integral of (5/x+(15)/(x^6))

\int (\frac{5}{x} + \frac{15}{x ^{6}}) d x

laplacetransform t-4 laplace transform

t - 4

(x+y)*y^'=2*x+2*y-3

(x + y) \cdot y^{^{'}} = 2 \cdot x + 2 \cdot y - 3

integral of (e^{x-1})/x

\int \frac{e ^{x - 1}}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(2x-sqrt(x)) ?
The derivative of ln(2x-sqrt(x)) is (4sqrt(x)-1)/(2sqrt(x)(2x-\sqrt{x))}
What is the first derivative of ln(2x-sqrt(x)) ?
The first derivative of ln(2x-sqrt(x)) is (4sqrt(x)-1)/(2sqrt(x)(2x-\sqrt{x))}