So differentiating term by term: ½ x ½ + (5/6)x -½ + ½x -3/2. The trick is to simplify the expression first: do the division (divide each term on the numerator by 3x ½. Therefore to differentiate x to the power of something you bring the power down to in front of the x, and then reduce the power by one. ĭifferentiating x to the power of somethingĢ) If y = kx n, dy/dx = nkx n-1(where k is a constant- in other words a number) If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x". There are a number of simple rules which can be used to allow us to differentiate many functions easily. It also allows us to find the rate of change of x with respect to y, which on a graph of y against x is the gradient of the curve. For example, it allows us to find the rate of change of velocity with respect to time (which is acceleration). Differentiation allows us to find rates of change.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |