What is the derivative of y=xln(sin^2(x)) ?

The derivative of y=xln(sin^2(x)) is ln(sin^2(x))+2xcot(x)

What is the first derivative of y=xln(sin^2(x)) ?

The first derivative of y=xln(sin^2(x)) is ln(sin^2(x))+2xcot(x)

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derivative of

y = x ln (sin^{2} (x))

ln (sin^{2} (x)) + 2 x cot (x)

Solution steps

\frac{d}{d x} (x ln (sin^{2} (x)))

Apply the Product Rule:

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

f = x, g = ln (sin^{2} (x))

= \frac{d x}{d x} ln (sin^{2} (x)) + \frac{d}{d x} (ln (sin^{2} (x))) x

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

\frac{d}{d x} (ln (sin^{2} (x))) = 2 cot (x)

= 1 \cdot ln (sin^{2} (x)) + 2 cot (x) x

Simplify

= ln (sin^{2} (x)) + 2 x cot (x)

y (x + 7) + \frac{d y}{d x} = 0

\int \frac{- 1}{\frac{1}{4} - x ^{2}} d x

(e^{t} (5 - 3 e^{- 2 t}))^{^{'}}

\int 12 x^{3} d x

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What is the derivative of y=xln(sin^2(x)) ?
The derivative of y=xln(sin^2(x)) is ln(sin^2(x))+2xcot(x)
What is the first derivative of y=xln(sin^2(x)) ?
The first derivative of y=xln(sin^2(x)) is ln(sin^2(x))+2xcot(x)