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Popular >

derivative of-x*ln(x)

Solution

\frac{d}{d x} (- x \cdot ln (x))

Solution

- ln (x) - 1

Solution steps

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

Take the constant out:

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

= - \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

Popular Examples

limit as x approaches 0 of (2.8^x-1)/x

x \to 0 lim (\frac{2. 8 ^{x} - 1}{x})

integral of 1/(2u)

\int \frac{1}{2 u} d u

121y^{''}+198y^'+65y=0

121 y^{^{''}} + 198 y^{^{'}} + 65 y = 0

derivative of (x^2-6x+8)^4 derivative of

(x^{2} - 6 x + 8)^{4}

(1+ln(x)+y/x)dx=(1-ln(x))dy

(1 + ln (x) + \frac{y}{x}) d x = (1 - ln (x)) d y

Frequently Asked Questions (FAQ)

What is the derivative of-x*ln(x) ?
The derivative of-x*ln(x) is -ln(x)-1
What is the first derivative of-x*ln(x) ?
The first derivative of-x*ln(x) is -ln(x)-1