when there is y^2 why does it become
2y * y'
2007-04-18 18:37:26 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
because y is the variable that you are differentiating, so you have to have something to solve for. Also, notice that when u integrate, u have dy in there...so the dy/dx has to come in somewhere to work backwards. Also, in the power rule, it says you also have to take the derivative of the thing that is being raised to the power and put outside. The derivative of y is y prime, so that is why it is out there
2007-04-18 18:42:32 · answer #1 · answered by dpmwcml 2 · 0⤊ 0⤋
Because when you differentiate y^2 with respect to x then you have to include a (dy/dx) times by the normal differential of y^2.
2007-04-18 18:42:04 · answer #2 · answered by Nick Solly 2 · 0⤊ 0⤋
It's short-cutting a step. Technically the differential is 2ydy. If you divide then by dx you have 1y(dy/dx) or 2ydy. However, implicit differentiation is also used when the independent variable is other than x (like t). then your differential gets divided by dt and you have 2y(dy/dt) or 2y*Vy (read v-sub-y)
2007-04-18 18:55:22 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋