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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int x e^{3} x d x

f (x) = (8 x + 9) (x^{3} - 6)

- 64 cos (2 x)

3 x (2 x - 1)^{3}

\frac{d}{d x} (1 - sec (x))

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