code: def partial_velocity(vel_vecs, gen_speeds, frame):
      """Returns a list of partial velocities with respect to the provided
      generalized speeds in the given reference frame for each of the supplied
      velocity vectors.
  
      The output is a list of lists. The outer list has a number of elements
      equal to the number of supplied velocity vectors. The inner lists are, for
      each velocity vector, the partial derivatives of that velocity vector with
      respect to the generalized speeds supplied.
  
      Parameters
      ==========
  
      vel_vecs : iterable
          An iterable of velocity vectors (angular or linear).
      gen_speeds : iterable
          An iterable of generalized speeds.
      frame : ReferenceFrame
          The reference frame that the partial derivatives are going to be taken
          in.
  
      Examples
      ========
  
      >>> from sympy.physics.vector import Point, ReferenceFrame
      >>> from sympy.physics.vector import dynamicsymbols
      >>> from sympy.physics.vector import partial_velocity
      >>> u = dynamicsymbols('u')
      >>> N = ReferenceFrame('N')
      >>> P = Point('P')
      >>> P.set_vel(N, u * N.x)
      >>> vel_vecs = [P.vel(N)]
      >>> gen_speeds = [u]
      >>> partial_velocity(vel_vecs, gen_speeds, N)
      [[N.x]]
  
      """
  
      if not iterable(vel_vecs):
          raise TypeError(
              "Velocity vectors must be contained in an iterable."
          )
  
      if not iterable(gen_speeds):
          raise TypeError(
              "Generalized speeds must be contained in an iterable"
          )
  
      vec_partials = []
      for vec in vel_vecs:
          partials = []
          for speed in gen_speeds:
              partials.append(vec.diff(speed, frame, var_in_dcm=False))
          vec_partials.append(partials)
  
      return vec_partials
  
file_path: sympy/sympy/physics/vector/functions.py
imports: from functools import reduce
  from sympy import sympify, diff, sin, cos, Matrix, symbols, Function, S, Symbol
  from sympy.integrals.integrals import integrate
  from sympy.simplify.trigsimp import trigsimp
  from .vector import Vector, _check_vector
  from .frame import CoordinateSym, _check_frame
  from .dyadic import Dyadic
  from .printing import vprint, vsprint, vpprint, vlatex, init_vprinting
  from sympy.utilities.iterables import iterable
  from sympy.utilities.misc import translate
label_desc: Use image node_id 8 for calling a global function with example usage: partial_velocity(vel_vecs, gen_speeds, frame) and returns: vec_partials