What is the d/(dθ)(cos(2θ)) ?

The d/(dθ)(cos(2θ)) is -sin(2θ)*2

What is the first d/(dθ)(cos(2θ)) ?

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

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\frac{d}{d θ} (cos (2 θ))

- sin (2 θ) \cdot 2

Solution steps

\frac{d}{d θ} (cos (2 θ))

Apply the chain rule:

- sin (2 θ) \frac{d}{d θ} (2 θ)

= - sin (2 θ) \frac{d}{d θ} (2 θ)

\frac{d}{d θ} (2 θ) = 2

= - sin (2 θ) \cdot 2

(x^{2} + 1) (\frac{d y}{d x}) + x y - x = 0

\frac{d}{d x} (\frac{1}{3} \cdot x^{3})

f (x) = e^{\frac{x}{( x - 9 )}}

\frac{d}{d s} (\frac{2 s ^{2}}{( s - 6 ) ^{3}})

\frac{1}{t} \frac{d y}{d t} - \frac{1}{1 + t ^{2}} = 0, y (0) = 1