What is (\partial)/(\partial θ)(ρsin(φ)sin(θ)) ?

The answer to (\partial)/(\partial θ)(ρsin(φ)sin(θ)) is ρsin(φ)cos(θ)

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(\partial)/(\partial θ)(ρsin(φ)sin(θ))

\frac{\partial}{\partial θ} (ρ sin (φ) sin (θ))

ρ sin (φ) cos (θ)

Solution steps

\frac{\partial}{\partial θ} (ρ sin (φ) sin (θ))

Treat

ρ, φ

as constants

Take the constant out:

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

= ρ sin (φ) \frac{\partial}{\partial θ} (sin (θ))

Apply the common derivative:

\frac{\partial}{\partial θ} (sin (θ)) = cos (θ)

= ρ sin (φ) cos (θ)

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What is (\partial)/(\partial θ)(ρsin(φ)sin(θ)) ?
The answer to (\partial)/(\partial θ)(ρsin(φ)sin(θ)) is ρsin(φ)cos(θ)