What is the d/(dθ)(cos^2(θ)) ?

The d/(dθ)(cos^2(θ)) is -sin(2θ)

What is the first d/(dθ)(cos^2(θ)) ?

The first d/(dθ)(cos^2(θ)) is -sin(2θ)

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\frac{d}{d θ} (cos^{2} (θ))

- sin (2 θ)

Solution steps

\frac{d}{d θ} (cos^{2} (θ))

Apply the chain rule:

2 cos (θ) \frac{d}{d θ} (cos (θ))

= 2 cos (θ) \frac{d}{d θ} (cos (θ))

\frac{d}{d θ} (cos (θ)) = - sin (θ)

= 2 cos (θ) (- sin (θ))

Simplify

2 cos (θ) (- sin (θ)) : - sin (2 θ)

= - sin (2 θ)

y^{3} - (2 x + 8) + 3 x y^{2} y^{^{'}} = 0

\frac{\partial}{\partial y} (3 x^{2} + 4 x y + y^{2})

\frac{\partial}{\partial x} (6 x y)

y^{^{''}} + y = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 4

\frac{d}{d x} ((tan (\frac{1}{x}))^{s e c (\frac{1}{x})})