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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

Simplify

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

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

\int 9 r cos (r) d r

y = x^{4 x}

\frac{d y}{d x} = (y^{2} - 4)

x \to - 2 lim (x + 1)

n = 1 \sum \infty 1 \cdot (\frac{1}{5})^{n}

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