What is implicit d/(dθ)(r(θ)),r(θ)=cos(θ)cot(θ) ?

The answer to implicit d/(dθ)(r(θ)),r(θ)=cos(θ)cot(θ) is d/(dθ)(r)=-cos(θ)-cot(θ)csc(θ)

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implicit d/(dθ)(r(θ)),r(θ)=cos(θ)cot(θ)

implicit derivative

\frac{d}{d θ} (r (θ)), r (θ) = cos (θ) cot (θ)

\frac{d}{d θ} (r) = - cos (θ) - cot (θ) csc (θ)

Solution steps

r = cos (θ) cot (θ)

Treat

r

r (θ)

Differentiate both sides:

\frac{d}{d θ} (r) = - cos (θ) - cot (θ) csc (θ)

Isolate

\frac{d}{d θ} (r) : \frac{d}{d θ} (r) = - cos (θ) - cot (θ) csc (θ)

\frac{d}{d θ} (r) = - cos (θ) - cot (θ) csc (θ)

f (x) = (x^{3} + 2) (x^{5} + 7 x^{2} + 3)

\frac{d}{d x} (\frac{x + 2}{x ^{2} + 5 x + 6})

f (x) = 2 + 5 x

(x - 3)^{2} \cdot (\frac{1}{2}) + 1

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

What is implicit d/(dθ)(r(θ)),r(θ)=cos(θ)cot(θ) ?
The answer to implicit d/(dθ)(r(θ)),r(θ)=cos(θ)cot(θ) is d/(dθ)(r)=-cos(θ)-cot(θ)csc(θ)