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

The derivative of (cos^2(x)dx) is d(-xsin(2x)+cos^2(x))

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

The first derivative of (cos^2(x)dx) is d(-xsin(2x)+cos^2(x))

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

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

Solution steps

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

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

\frac{d x}{d x} = 1

= d ((- sin (2 x)) x + 1 \cdot cos^{2} (x))

Simplify

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

x \to 0 - lim (- \frac{1}{x ^{3}})

\int_{5}^{10} \frac{y}{y ^{2} - y - 2} d y

8 sec (x)

x \to - a lim (x)

\frac{d}{d x} ((\frac{x}{x + 5})^{4})

What is the derivative of (cos^2(x)dx) ?
The derivative of (cos^2(x)dx) is d(-xsin(2x)+cos^2(x))
What is the first derivative of (cos^2(x)dx) ?
The first derivative of (cos^2(x)dx) is d(-xsin(2x)+cos^2(x))