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Popular >

derivative of xln(x/4)

Solution

\frac{d}{d x} (x ln (\frac{x}{4}))

Solution

ln (\frac{x}{4}) + 1

Solution steps

\frac{d}{d x} (x ln (\frac{x}{4}))

Apply the Product Rule:

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

f = x, g = ln (\frac{x}{4})

= \frac{d x}{d x} ln (\frac{x}{4}) + \frac{d}{d x} (ln (\frac{x}{4})) x

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

\frac{d}{d x} (ln (\frac{x}{4})) = \frac{1}{x}

= 1 \cdot ln (\frac{x}{4}) + \frac{1}{x} x

Simplify

1 \cdot ln (\frac{x}{4}) + \frac{1}{x} x : ln (\frac{x}{4}) + 1

= ln (\frac{x}{4}) + 1

Popular Examples

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\frac{2}{s ^{2}}

limit as x approaches 5 of 10

x \to 5 lim (10)

integral of sin^7(xco)s^4x

\int sin^{7} (x co) s^{4} x d x

(\partial)/(\partial x)(6y^9x^5-5y^8x^4)

\frac{\partial}{\partial x} (6 y^{9} x^{5} - 5 y^{8} x^{4})

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x \to \infty lim (- x R (x) C (x))

Frequently Asked Questions (FAQ)

What is the derivative of xln(x/4) ?
The derivative of xln(x/4) is ln(x/4)+1
What is the first derivative of xln(x/4) ?
The first derivative of xln(x/4) is ln(x/4)+1