What is the derivative of (4+ln(2x)/(2020+x)) ?

The derivative of (4+ln(2x)/(2020+x)) is (2020-3x-xln(2x))/(x(2020+x)^2)

What is the first derivative of (4+ln(2x)/(2020+x)) ?

The first derivative of (4+ln(2x)/(2020+x)) is (2020-3x-xln(2x))/(x(2020+x)^2)

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\frac{d}{d x} (\frac{4 + ln ( 2 x )}{2020 + x})

\frac{2020 - 3 x - x ln ( 2 x )}{x ( 2020 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 + ln ( 2 x )}{2020 + x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 4 + ln ( 2 x ) ) ( 2020 + x ) - \frac{d}{d x} ( 2020 + x ) ( 4 + ln ( 2 x ) )}{( 2020 + x ) ^{2}}

\frac{d}{d x} (4 + ln (2 x)) = \frac{1}{x}

\frac{d}{d x} (2020 + x) = 1

= \frac{\frac{1}{x} ( 2020 + x ) - 1 \cdot ( 4 + ln ( 2 x ) )}{( 2020 + x ) ^{2}}

Simplify

\frac{\frac{1}{x} ( 2020 + x ) - 1 \cdot ( 4 + ln ( 2 x ) )}{( 2020 + x ) ^{2}} : \frac{2020 - 3 x - x ln ( 2 x )}{x ( 2020 + x ) ^{2}}

= \frac{2020 - 3 x - x ln ( 2 x )}{x ( 2020 + x ) ^{2}}

e^{4 x}, 3

7 arctan (x - 1 + x^{2})

8 e^{- 6 t} cos (4 t + 30)

\int_{- \infty}^{0} \frac{1}{4 - 10 x} d x

f (x) = - 2 x^{3}, at x = 1

What is the derivative of (4+ln(2x)/(2020+x)) ?
The derivative of (4+ln(2x)/(2020+x)) is (2020-3x-xln(2x))/(x(2020+x)^2)
What is the first derivative of (4+ln(2x)/(2020+x)) ?
The first derivative of (4+ln(2x)/(2020+x)) is (2020-3x-xln(2x))/(x(2020+x)^2)