What is the d/(dθ)(cos(θ)-θsin(θ)) ?

The d/(dθ)(cos(θ)-θsin(θ)) is -2sin(θ)-θcos(θ)

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

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

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\frac{d}{d θ} (cos (θ) - θ sin (θ))

- 2 sin (θ) - θ cos (θ)

Solution steps

\frac{d}{d θ} (cos (θ) - θ sin (θ))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

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

= - sin (θ) - (sin (θ) + θ cos (θ))

Simplify

= - 2 sin (θ) - θ cos (θ)

9 x^{2}, 8 x^{4} - 8 x^{2}

\frac{d y}{d x} + 2 x^{2} = 0

\int \frac{e ^{x}}{e ^{x} + 6} d x

x e^{- \frac{1}{x}}

x (e^{\frac{y}{x}} - 1) \frac{d y}{d x} = e^{\frac{y}{x}} (y - x)

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