What is the derivative of xln(sin(x)) ?

The derivative of xln(sin(x)) is ln(sin(x))+xcot(x)

What is the first derivative of xln(sin(x)) ?

The first derivative of xln(sin(x)) is ln(sin(x))+xcot(x)

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

ln (sin (x)) + x cot (x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (sin (x))

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

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

\frac{d}{d x} (ln (sin (x))) = cot (x)

= 1 \cdot ln (sin (x)) + cot (x) x

Simplify

= ln (sin (x)) + x cot (x)

\int_{0}^{\infty} e^{- x} d x

\int x cos (x^{2}) d x

f (x) = 9 + \frac{3}{x}

\int (\frac{x}{x ^{2} + 4}) d x

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

What is the derivative of xln(sin(x)) ?
The derivative of xln(sin(x)) is ln(sin(x))+xcot(x)
What is the first derivative of xln(sin(x)) ?
The first derivative of xln(sin(x)) is ln(sin(x))+xcot(x)