What is the d/(dθ)(cos(θ)sin(θ)) ?

The d/(dθ)(cos(θ)sin(θ)) is cos(2θ)

What is the first d/(dθ)(cos(θ)sin(θ)) ?

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

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\frac{d}{d θ} (cos (θ) sin (θ))

cos (2 θ)

Solution steps

\frac{d}{d θ} (cos (θ) sin (θ))

Apply the Product Rule:

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

f = cos (θ), g = sin (θ)

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

\frac{d}{d θ} (sin (θ)) = cos (θ)

= (- sin (θ)) sin (θ) + cos (θ) cos (θ)

Simplify

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

= cos (2 θ)

\frac{1}{2 t - 1}

\int (1 - t) (7 + t^{2}) d t

x \to 1 + lim (2 - x)

\frac{\partial}{\partial x} (\frac{x + y}{1 + y ^{2}})

\int \frac{( ( ln ( x ) ) ^{2} )}{x} d x

What is the d/(dθ)(cos(θ)sin(θ)) ?
The d/(dθ)(cos(θ)sin(θ)) is cos(2θ)
What is the first d/(dθ)(cos(θ)sin(θ)) ?
The first d/(dθ)(cos(θ)sin(θ)) is cos(2θ)