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

The derivative of sin^2(xcos(x)) is sin(2x)cos(x)-sin^3(x)

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

The first derivative of sin^2(xcos(x)) is sin(2x)cos(x)-sin^3(x)

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

sin (2 x) cos (x) - sin^{3} (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

= sin (2 x) cos (x) + (- sin (x)) sin^{2} (x)

Simplify

sin (2 x) cos (x) + (- sin (x)) sin^{2} (x) : sin (2 x) cos (x) - sin^{3} (x)

= sin (2 x) cos (x) - sin^{3} (x)

y^{^{'}} = 2 x y^{2}

\int 5 16 - 2 x - 10 d x

f (x) = 7 e^{x}

\frac{d}{d x} (\frac{4 b}{a} x a^{2} - x^{2})

\frac{x ^{\frac{3}{2}}}{3}

What is the derivative of sin^2(xcos(x)) ?
The derivative of sin^2(xcos(x)) is sin(2x)cos(x)-sin^3(x)
What is the first derivative of sin^2(xcos(x)) ?
The first derivative of sin^2(xcos(x)) is sin(2x)cos(x)-sin^3(x)