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

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

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

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

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

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

Solution steps

\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

= \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

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

Simplify

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

\frac{\partial}{\partial x} (x y)

\frac{10}{( x ^{2} - 7 ) ^{4}}

y = sec (x), (\frac{π}{3}, 2)

\frac{7}{6 s ( s + \frac{2}{9} )}

\int ln (x + 9) d x

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