MATH 6A Lecture Notes - Lecture 12: Directional Derivative, Differentiable Function, Unit Vector

• School: UCSB
• Department: Mathematics
• Course: MATH 6A
• Professor: Fryer

Document Summary

Then its derivative (which is also the gradient. This is a function and its gradient is. Recall that the geometric meaning of etc. is the rate of the change of in the. The directional derivative of in direction , where is a unit vector at the point , is given by. Exercise: compute the directional derivative of in the direction (note: you need to normalize first because must be a unit vector) Theorem 2. 9: let be a differentiable function on (or ) and suppose for then the direction of the largest rate of increase of at is in direction. Interpret in terms of the angle between and ; this is maximized when , ie and are parallel. , eg theorem 2. 10: let be a differentiable function, and is a parametrization of one of its level curves. If , then is perpendicular to the tangent vector.