Question

Hello
in session 87 of Multivariable calculus.
question 2:
Differentiate A with respect to R
\( A=\frac{1}{4 \pi} \int _{0}^{2 \pi} \int _{0}^{\pi}(R sin (\phi) cos(\theta) , R sin (\phi) sin(\theta) + R cos (\phi)) \ sin (\phi) \ d\phi d\theta \)
does someone could explain to me the transition from A to dA/dR given in the solution to the problem:

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/4.-triple-integrals-and-surface-integrals-in-3-space/part-b-flux-and-the-divergence-theorem/session-87-diffusion-equation/
solution:
http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/4.-triple-integrals-and-surface-integrals-in-3-space/part-b-flux-and-the-divergence-theorem/session-87-diffusion-equation/MIT18_02SC_pb_87_comb.pdf

\( u_x=\frac{\partial u}{\partial x} \ \text{ or } \ u_x= \frac{\partial u}{\partial R} \text{ x component ? } \)
\( \frac{d A}{d R}=\frac{1}{4 \pi} \int _{0}^{2 \pi} \int _{0}^{\pi}(u_x sin (\phi) cos(\theta) + u_y sin (\phi) sin(\theta) + u_z cos (\phi)) \ sin (\phi) \ d\phi d\theta \\
\text{2) secondary why the notation was not } \frac{\partial A}{\partial R} \\

\text{beware latex header is not $, Latex header:\( Latex Queue: \) } \)