What is the derivative of f(x)=(ln(x))/(38+x) ?

The derivative of f(x)=(ln(x))/(38+x) is (38+x-xln(x))/(x(38+x)^2)

What is the first derivative of f(x)=(ln(x))/(38+x) ?

The first derivative of f(x)=(ln(x))/(38+x) is (38+x-xln(x))/(x(38+x)^2)

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derivative of

f (x) = \frac{ln ( x )}{38 + x}

\frac{38 + x - x ln ( x )}{x ( 38 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{38 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) ( 38 + x ) - \frac{d}{d x} ( 38 + x ) ln ( x )}{( 38 + x ) ^{2}}

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (38 + x) = 1

= \frac{\frac{1}{x} ( 38 + x ) - 1 \cdot ln ( x )}{( 38 + x ) ^{2}}

Simplify

\frac{\frac{1}{x} ( 38 + x ) - 1 \cdot ln ( x )}{( 38 + x ) ^{2}} : \frac{38 + x - x ln ( x )}{x ( 38 + x ) ^{2}}

= \frac{38 + x - x ln ( x )}{x ( 38 + x ) ^{2}}

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e x p an d (x - 1)^{2} (x - 2) (x - 4)

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

What is the derivative of f(x)=(ln(x))/(38+x) ?
The derivative of f(x)=(ln(x))/(38+x) is (38+x-xln(x))/(x(38+x)^2)
What is the first derivative of f(x)=(ln(x))/(38+x) ?
The first derivative of f(x)=(ln(x))/(38+x) is (38+x-xln(x))/(x(38+x)^2)