What is (\partial)/(\partial a)(a/(sin(θ))) ?

The answer to (\partial)/(\partial a)(a/(sin(θ))) is csc(θ)

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(\partial)/(\partial a)(a/(sin(θ)))

\frac{\partial}{\partial a} (\frac{a}{sin ( θ )})

csc (θ)

Solution steps

\frac{\partial}{\partial a} (\frac{a}{sin ( θ )})

Simplify

\frac{a}{sin ( θ )} : a csc (θ)

= \frac{\partial}{\partial a} (a csc (θ))

Treat

θ

as a constant

Take the constant out:

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

= csc (θ) \frac{\partial}{\partial a} (a)

Apply the common derivative:

\frac{\partial}{\partial a} (a) = 1

= csc (θ) \cdot 1

Simplify

= csc (θ)

What is (\partial)/(\partial a)(a/(sin(θ))) ?
The answer to (\partial)/(\partial a)(a/(sin(θ))) is csc(θ)