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Popular >

derivative of (x-4)ln(4-x)

Solution

derivative of

(x - 4) ln (4 - x)

Solution

ln (4 - x) + 1

Solution steps

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

Apply the Product Rule:

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

f = x - 4, g = ln (4 - x)

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

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

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

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

Simplify

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

= ln (4 - x) + 1

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x \to - 1 + lim (ln (x + 1))

Frequently Asked Questions (FAQ)

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