[WClayFerguson]

Any change in direction is an acceleration (by definition). Even an object moving in a perfect circle at constant radians per second is nonetheless undergoing a constant non-zero acceleration just due to change in direction. Acceleration is any change in a velocity vector, including simply a change in direction, and requires a force (if the object has mass)

[Ace17]

Yes, obviously. But the message seemed to say that the constant speed of light implied that the derivative of the velocity with respect to time had to be zero.

[WClayFerguson]

In physics speed means the magnitude of the velocity vector. Velocity is the first derivative of position with respect to time, and it's a vector in 3D space (technically 4D). If you change the orientation of that vector (direction change) that is always an acceleration even if the magnitude of the vector doesn't change.

So when light goes thru a gravitational field it doesn't change direction (EVEN though gravitational lensing is happening, from the perspective of an observer). If it did change direction that would be synonymous with an acceleration, and light never accelerates.