What is the d/(dθ)(1+cos(θ)) ?

The d/(dθ)(1+cos(θ)) is -sin(θ)

What is the first d/(dθ)(1+cos(θ)) ?

The first d/(dθ)(1+cos(θ)) is -sin(θ)

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\frac{d}{d θ} (1 + cos (θ))

- sin (θ)

Solution steps

\frac{d}{d θ} (1 + cos (θ))

Apply the Sum/Difference Rule:

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

= \frac{d}{d θ} (1) + \frac{d}{d θ} (cos (θ))

\frac{d}{d θ} (1) = 0

\frac{d}{d θ} (cos (θ)) = - sin (θ)

= 0 - sin (θ)

Simplify

= - sin (θ)

\frac{d}{d x} (cos (x))

x \frac{d y}{d x} - 2 y = x y^{3}

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\int (9 x^{2} - 8 x + 4) d x