What is the derivative of xln(5x) ?

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

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

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

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

ln (5 x) + 1

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (5 x)

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

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

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

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

Simplify

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

= ln (5 x) + 1

3 x^{2} - 4 x + 6, at x = 2

y^{^{''}} + 4 y = 0, y (0) = 1, y (1) = 0

\frac{d}{d t} (a e^{t} cos (2 t) + b e^{t} sin (2 t))

x \to 0 lim ((1 + x)^{2} - 1)

x \to 1 lim (6 x^{2} + 1)

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