Question

Is the gradient the same as the derivative?

Answer 1

1. Vectors: At a given point, the gradient is defined as a vector that is tangent to the function. A derivative is another name for a gradient function.
2. The derivative is also known as the rate of change of a function.
3. The gradient of a function, $f(x,y),$in two dimensions, is defined as: $\text{grad}f(x,y)=\nabla f(x,y)=\frac{\partial f}{\partial x}i+\frac{\partial f}{dy}i$ where $\nabla$ vector operator.
4. The gradient will be in the direction of the steepest ascent of the function from that point.
5. To put it another way, the gradient is a vector that has a quantity specified by the derivative and points in the direction where the rate of change is greatest.

Hence, the vector derivative gives the gradient.