Derivatives of Higher Order
Derivatives of Higher Order
Derivatives of functions are also functions, therefore can be differentiated again.
ex.
Calculus
Forum reference:
Book page:
http://course-notes.org/Calculus
Implicit Differentiation
Implicit Differentiation
So far, all the functions being differentiated are explicit functions, meaning that one of the variables was specifically given in terms of the other variable.
ex.
The Slope Of a Curve
The Slope Of a Curve:
Consider the graph:
The slope of the curve is the slope of the secant line between point A and another point P on the graph.
Differentiation And Derivatives
Differentiation And Derivatives:
The Differentiation of function f at x is:
If this limit exists, then it is called the derivative of function f at x, which is denoted by f '(x).
Tangent and Normal Lines of Curves
Tangent and Normal Lines of Curves:
From the given definitions; f '(x) is the slope of the tangent line of a curve at a certain point. From the point slope formula, the formula for the tangent line of a curve at a given point is:
y - y0 = f '(x0)(x - x0)
Derivative of a Constant
Derivative of a Constant:
If function f is a constant c; f(x) = c then f' (x) = 0.
Power Rule
Power Rule:
If function f is f(x) = xn, where n is any integer, then f' (x) = n·xn-1.
Constant Multiple Rule
Constant Multiple Rule:
If g is a differentiable function and c is a real number;
f(x) = c·g(x) then, f '(x) = c· g '(x).
Derivative of a Sum or Difference
Derivative of a Sum or Difference:
If g and h are differentiable functions and f is a function such that:
f(x) = g(x) + h(x) then f '(x) = g '(x) + h '(x).
f(x) = g(x) - h(x) then f '(x) = g '(x) - h '(x).
Derivative of a Product
Derivative of a Product:
If g and h are differentiable functions and f is a function such that:
f(x) = g(x) · h(x) then f '(x) = g(x) ·h '(x) + g '(x) · h(x)
Pages
Need Help?
We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.
For general help, questions, and suggestions, try our dedicated support forums.
If you need to contact the Course-Notes.Org web experience team, please use our contact form.
Need Notes?
While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!
