What is the derivative of xln(x) ?

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

What is the first derivative of xln(x) ?

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

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derivative of

x ln (x)

ln (x) + 1

Solution steps

\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)

= \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}

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

Simplify

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

= ln (x) + 1

\int \frac{1}{( x - 3 ) ( 2 x + 1 ) ( x ^{2} + x + 4 )} d x

(x + 5 x) (x^{\frac{3}{2}} - x)

- 2 x^{4} + 7 x e^{x}

\int (b - ∣ x ∣)^{2} d x

f (x) = - 8 x^{2} - 7, at x = 1

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