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

The derivative of cos^2(xcos(2x)) is (-sin(4x)-8cos^3(x)sin(x))/2

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

The first derivative of cos^2(xcos(2x)) is (-sin(4x)-8cos^3(x)sin(x))/2

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

\frac{- sin ( 4 x ) - 8 cos ^{3} ( x ) sin ( x )}{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(- sin (2 x)) cos (2 x) + (- sin (2 x) \cdot 2) cos^{2} (x) : \frac{- sin ( 4 x ) - 8 cos ^{3} ( x ) sin ( x )}{2}

= \frac{- sin ( 4 x ) - 8 cos ^{3} ( x ) sin ( x )}{2}

f (x) = 5 x^{3} - 3 x^{5}

S (r) = r - rr

p (x) = 6 x^{2} + 5 x^{3} + 7 - x^{5}

f (x) = lo g_{x} (12)

y = x \cdot e^{- x}

What is the derivative of cos^2(xcos(2x)) ?
The derivative of cos^2(xcos(2x)) is (-sin(4x)-8cos^3(x)sin(x))/2
What is the first derivative of cos^2(xcos(2x)) ?
The first derivative of cos^2(xcos(2x)) is (-sin(4x)-8cos^3(x)sin(x))/2