What is the derivative of sin^2(xcot(5x)) ?

The derivative of sin^2(xcot(5x)) is sin(2x)cot(5x)-5csc^2(5x)sin^2(x)

What is the first derivative of sin^2(xcot(5x)) ?

The first derivative of sin^2(xcot(5x)) is sin(2x)cot(5x)-5csc^2(5x)sin^2(x)

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\frac{d}{d x} (sin^{2} (x) cot (5 x))

sin (2 x) cot (5 x) - 5 csc^{2} (5 x) sin^{2} (x)

Solution steps

\frac{d}{d x} (sin^{2} (x) cot (5 x))

Apply the Product Rule:

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

f = sin^{2} (x), g = cot (5 x)

= \frac{d}{d x} (sin^{2} (x)) cot (5 x) + \frac{d}{d x} (cot (5 x)) sin^{2} (x)

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

\frac{d}{d x} (cot (5 x)) = - csc^{2} (5 x) \cdot 5

= sin (2 x) cot (5 x) + (- csc^{2} (5 x) \cdot 5) sin^{2} (x)

Simplify

= sin (2 x) cot (5 x) - 5 csc^{2} (5 x) sin^{2} (x)

\frac{4 s - 36}{s ^{2} - 8 s + 15}

(0.5) (1)

\frac{d}{d u} (ln (u))

(y^{2} - 2 x y) d x + x^{2} d y = 0

\frac{d}{d x} (e^{x^{2} - 2 x})

What is the derivative of sin^2(xcot(5x)) ?
The derivative of sin^2(xcot(5x)) is sin(2x)cot(5x)-5csc^2(5x)sin^2(x)
What is the first derivative of sin^2(xcot(5x)) ?
The first derivative of sin^2(xcot(5x)) is sin(2x)cot(5x)-5csc^2(5x)sin^2(x)