AP Calculus

AP Calculus Calculus is a branch of Mathematics which deals with the methods of Derivation and Integration. These two methods are the sub-branches of Calculus and are used to solve functions based on them. AP Calculus is the Advanced Placement Examination in Calculus which is given in order to test a high school student in Calculus questions. Example 1: Find the derivative of the given function, f(x) = x5 + 2x3 Power rule of the Derivatives - d f(xn)/dx = n*xn-1 Given function: x5 + 2x3 Applying the above formula for every term of the function, we get Derivative of the given function - d f(x)/dx= d (x5)/dx +2*d(x3)/dx df(x)/dx = 5 *x5-1 + 2 * 3 * x3-1 d f(x)/dx = 5x4 + 6x2 Hence the derivative of the function f(x) =x5 + 2x3 is 5x4 + 6x2 Example 2: Calculate the definite integral value of the function, f(x) = 4x3 - 3x2 and x ranging from 0 to 2. xn dx= x(n+1)/ (n+1) Apply the above formula for the given function, we get (fx) dx = 4 *x3+1/(3 + 1) 3 *x2+1/(2 + 1) f(x)dx = x4 x3 First substitute x = 0 and x= 2 in the above answer. When x= 0, f(x) dx= 04 03 = 0 When x=2, f(x)dx= 24 23 = 8 Now subtract 8 - 0 = 8 Hence the definite integral of the given f(x) is 8.