Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
You take the derivative using only one variable. The other variables act as constants.
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
First find the derivative of each term. The derivative of any constant is zero, so d(1)/dx=0. To find the derivative of cos2x, use the chain rule. d(cos2x)/dx=-sin(2x)(2)=-2sin(2x) So the answer is 0-2sinx, or simply -2sinx
Find the derivative
I'll get you started. Using the definition of the derivative:For f(x) = xsinx this gives:Recall thatFrom here you should be able to finish it out. Post back if you're still having difficulties.
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
Oh, dude, the third derivative of ln(x) is -2/(x^3). But like, who really needs to know that, right? I mean, unless you're planning on impressing your calculus teacher or something. Just remember, math is like a puzzle, except no one actually wants to put it together.
You take the derivative using only one variable. The other variables act as constants.
you have to first find the derivative of the original function. You then make the derivative equal to zero and solve for x.
At the point of inflexion:the first derivative must be zero. the second derivative must be zero, if the next derivative is zero then the one following that must also be zero.
First find the derivative of each term. The derivative of any constant is zero, so d(1)/dx=0. To find the derivative of cos2x, use the chain rule. d(cos2x)/dx=-sin(2x)(2)=-2sin(2x) So the answer is 0-2sinx, or simply -2sinx
You will find several formulae in the Wikipedia article on "derivative".
The min and max is when the first derivative , or slope at any point, is zero. For f of x = 2x first derivative is 2, so this is constant slope with no min or max as this is not zero; min is thus negative infinity and max is infinity
The derivative at any point in a curve is equal to the slope of the line tangent to the curve at that point. Doing it in terms of the actual expression of the curve, find the derivative of the curve, then plug the x-value of the point into the derivative to find the derivative at that point.
Find the derivative of Y and then divide that by the derivative of A