What is the d/(dθ)((x(θ))(a(θ-sin(θ)))) ?

The d/(dθ)((x(θ))(a(θ-sin(θ)))) is ax(2θ-θcos(θ)-sin(θ))

What is the first d/(dθ)((x(θ))(a(θ-sin(θ)))) ?

The first d/(dθ)((x(θ))(a(θ-sin(θ)))) is ax(2θ-θcos(θ)-sin(θ))

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\frac{d}{d θ} ((x (θ)) (a (θ - sin (θ))))

a x (2 θ - θ cos (θ) - sin (θ))

Solution steps

\frac{d}{d θ} ((x (θ)) (a (θ - sin (θ))))

Treat

a, x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x a \frac{d}{d θ} (θ (θ - sin (θ)))

Apply the Product Rule:

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

f = θ, g = θ - sin (θ)

= x a (\frac{d}{d θ} (θ) (θ - sin (θ)) + \frac{d}{d θ} (θ - sin (θ)) θ)

\frac{d}{d θ} (θ) = 1

\frac{d}{d θ} (θ - sin (θ)) = 1 - cos (θ)

= x a (1 \cdot (θ - sin (θ)) + (1 - cos (θ)) θ)

Simplify

x a (1 \cdot (θ - sin (θ)) + (1 - cos (θ)) θ) : a x (2 θ - θ cos (θ) - sin (θ))

= a x (2 θ - θ cos (θ) - sin (θ))

\frac{k ( s + 4 )}{s ( s + 1 ) ( s + 3 )}

(2 - x - 4)^{2}

- e^{x} (e^{2 x} - e^{- x})

\frac{x - 2}{( x + 2 ) ( x - 4 )}

(3 sin^{2} (θ)) (1 + sin^{2} (θ))

What is the d/(dθ)((x(θ))(a(θ-sin(θ)))) ?
The d/(dθ)((x(θ))(a(θ-sin(θ)))) is ax(2θ-θcos(θ)-sin(θ))
What is the first d/(dθ)((x(θ))(a(θ-sin(θ)))) ?
The first d/(dθ)((x(θ))(a(θ-sin(θ)))) is ax(2θ-θcos(θ)-sin(θ))