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

The derivative of cos^2(xtan(x)) is cos(2x)

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

The first derivative of cos^2(xtan(x)) is cos(2x)

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

cos (2 x)

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = cos (x), g = sin (x)

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

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

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

= (- sin (x)) sin (x) + cos (x) cos (x)

Simplify

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

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