What is the derivative of 5xln(x) ?

The derivative of 5xln(x) is 5(ln(x)+1)

What is the first derivative of 5xln(x) ?

The first derivative of 5xln(x) is 5(ln(x)+1)

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

5 (ln (x) + 1)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = ln (x)

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

\frac{d x}{d x} = 1

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

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

Simplify

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

= 5 (ln (x) + 1)

\int \frac{1}{5 x - 3} d x

h \to 0 lim (\frac{( 2 ^{h} - 1 )}{h})

\frac{d}{d x} ((3 + 2 x) e^{- 2 x})

\frac{d}{d x} (π x^{2})

\int \frac{x ^{2} + 24 x ^{3}}{x} d x

What is the derivative of 5xln(x) ?
The derivative of 5xln(x) is 5(ln(x)+1)
What is the first derivative of 5xln(x) ?
The first derivative of 5xln(x) is 5(ln(x)+1)