Today in class we went over the question from yesterday, number 5 on the worksheet called "Chain Rule combined with other differentiation rules." We learned that a circle is really two different explicit functions, one negative and one positive. The implicit function is x^2 + y^2 = 25.
We then did four review problems of composite functions. We reviewed how to find the derivative of tan(f(x)), sec(g(x)), e^(h(x)), and (f(x))^N. Then we started learning Implicit Differentiation. Using the slow method, we found the derivative of x^2 + (f(x))^2 =25, which is -x/f(x). The faster method involved using "y" instead of f(x), which meant that instead of using f'(x) we used dy/dx. The slow and fast methods are the same: they just use different notation.
We did a second example on the board and then we completed a worksheet in class called "Implicit Differentiation practice." We discussed that since you write the derivative of y^3 as 3y^2*(dy/dx), you can also write the derivative of x^3 as 3x^2* (dx/dx). We also said Newton would be interested in doing calculus for ellipses because the planets' orbits are ellipses, and he was fascinated with the planets.
1 comment:
Today in class we went over the question from yesterday, number 5 on the worksheet called "Chain Rule combined with other differentiation rules." We learned that a circle is really two different explicit functions, one negative and one positive. The implicit function is x^2 + y^2 = 25.
We then did four review problems of composite functions. We reviewed how to find the derivative of tan(f(x)), sec(g(x)), e^(h(x)), and (f(x))^N. Then we started learning Implicit Differentiation. Using the slow method, we found the derivative of x^2 + (f(x))^2 =25, which is -x/f(x). The faster method involved using "y" instead of f(x), which meant that instead of using f'(x) we used dy/dx. The slow and fast methods are the same: they just use different notation.
We did a second example on the board and then we completed a worksheet in class called "Implicit Differentiation practice." We discussed that since you write the derivative of y^3 as 3y^2*(dy/dx), you can also write the derivative of x^3 as 3x^2* (dx/dx). We also said Newton would be interested in doing calculus for ellipses because the planets' orbits are ellipses, and he was fascinated with the planets.
Post a Comment