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Popular >

derivative of (5+xln(x))

Solution

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

Solution

ln (x) + \frac{5 + x}{x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 5 + x, g = ln (x)

= \frac{d}{d x} (5 + x) ln (x) + \frac{d}{d x} (ln (x)) (5 + x)

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

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

= 1 \cdot ln (x) + \frac{1}{x} (5 + x)

Simplify

1 \cdot ln (x) + \frac{1}{x} (5 + x) : ln (x) + \frac{5 + x}{x}

= ln (x) + \frac{5 + x}{x}

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Frequently Asked Questions (FAQ)

What is the derivative of (5+xln(x)) ?
The derivative of (5+xln(x)) is ln(x)+(5+x)/x
What is the first derivative of (5+xln(x)) ?
The first derivative of (5+xln(x)) is ln(x)+(5+x)/x