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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\frac{d}{d x} (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

x \to π lim (\frac{tan ( x )}{x})

\int_{7}^{\infty} x e^{- 5 x} d x

\frac{d}{d x} (4 x^{3} - 102 x^{2} + 840 x + 520)

y^{^{''}} + 5 y^{^{'}} + 6 y = 1 + 2 t + 3 t^{2}

25 (x^{2} - y^{2})

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