To solve derivatives of monomials, use as the general term:
When f(x)=xn, f'(x)[the derivative]=nxn-1Example 1: 2x6 = 2(6)x6-1
= 12x5
Example 2: 3x = 3(1)x1-1
=3x0
=3
You will find several formulae in the Wikipedia article on "derivative".
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
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The purpose of finding a derivative is to find the instantaneous rate of change. In addition, taking the derivative is used in integration by parts.
The derivative of x^n is nx^(n-1) any n. The derivative of x^4 is 4x^3.
The derivative of sin(x) is cos(x).
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
Find the derivative
The inverse operation to the derivative. Also called the integral. If you're given the derivative of a function, you can find the function again by performing the antiderivative. Many answers will be possible, all differing by a single number, so you normally add a general constant to the end. Example : The derivative of 6x^2 is 12x. The antiderivative of 12x is 6x^2 + any number.
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.
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)