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Popular >

derivative of (x-1(ln(x)))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x - 1, g = ln (x)

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(3sin(4x))

\frac{\partial}{\partial x} (3 sin (4 x))

derivative of-(x^4/4)

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

(dy)/(y^3)=x^{-2}dx

\frac{d y}{y ^{3}} = x^{- 2} d x

integral of (3^x)/(1+9^x)

\int \frac{3 ^{x}}{1 + 9 ^{x}} d x

derivative of-(12)/(x^5)derivative of

- \frac{12}{x ^{5}}

Frequently Asked Questions (FAQ)

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