What is the d/(dθ)(θcos(θ)) ?

The d/(dθ)(θcos(θ)) is cos(θ)-θsin(θ)

What is the first d/(dθ)(θcos(θ)) ?

The first d/(dθ)(θcos(θ)) is cos(θ)-θsin(θ)

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\frac{d}{d θ} (θ cos (θ))

cos (θ) - θ sin (θ)

Solution steps

\frac{d}{d θ} (θ cos (θ))

Apply the Product Rule:

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

f = θ, g = cos (θ)

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

\frac{d}{d θ} (θ) = 1

\frac{d}{d θ} (cos (θ)) = - sin (θ)

= 1 \cdot cos (θ) + (- sin (θ)) θ

Simplify

= cos (θ) - θ sin (θ)

\frac{d}{d x} ((x - 1) ∣ x - 1 ∣)

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

\frac{d}{d x} (k x^{x})

\frac{d}{d x} (\frac{x ^{2}}{( 4 + x )})

\frac{d}{d x} (\frac{3 x + 4}{3 x - 4})