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

The derivative of sin^2(x)(cos(x))^2 is (sin(4x))/2

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

The first derivative of sin^2(x)(cos(x))^2 is (sin(4x))/2

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derivative of

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

\frac{sin ( 4 x )}{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

sin (2 x) cos^{2} (x) + (- sin (2 x)) sin^{2} (x) : \frac{sin ( 4 x )}{2}

= \frac{sin ( 4 x )}{2}

5 x^{2} y^{2}

\frac{- 2 y}{x}

\frac{( x ^{3} - x )}{( x ^{2} )}

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

\frac{d}{d x} (\frac{sin ^{22} ( x )}{cos ^{2} ( x )})

What is the derivative of sin^2(x)(cos(x))^2 ?
The derivative of sin^2(x)(cos(x))^2 is (sin(4x))/2
What is the first derivative of sin^2(x)(cos(x))^2 ?
The first derivative of sin^2(x)(cos(x))^2 is (sin(4x))/2