Class Name: Derivatives
Method Name: calcDerivative
Parameters: String,int,int
Returns: int
Implement a class Derivatives which contains a method calcDerivative. The
method takes a String representing a polynomial, and two ints, k and x. The
method returns the kth derivative of the polynomial evaluated at x.
The first derivative of any term of a polynomial is:
1st derivative of (a*x^n) = (a*n*x^(n1)).
The first derivative of any polynomial is the sum of the first derivatives of
the polynomial's terms.
The kth derivative of a polynomial is the 1st derivative of the (k1)th
derivative of the polynomial.
The 0th derivative of a polynomial is the polynomial itself.
The String will be of the form:
"a1*x^n1+a2*x^n2+...."
There are no spaces.
All the a's are nonnegative integers less than 20
All the n's are unique nonnegative integers less than 10.
The String is at most 50 characters and at least 5 characters.
Here is the method signature:
public int calcDerivative(String poly,int k,int x);
poly is of the correct form.
k is an integer between 0 and 10, inclusive.
x is an integer between 10 and 10, inclusive.
Examples:
*If poly="3*x^3+2*x^1+2*x^0", k=1, and x=1:
The first derivative is: 3*3*x^(31)+2*1*x^(11)+0*2*x^(01)=9*x^2+2*x^0.
The first derivative evaluated at x=1 is: 9*1^2+2*1^0=11
So the method returns 11.
*If poly="2*x^5+3*x^2", k=2, and x=2,
The first derivative is: 5*2*x^(51)+3*2*x^(21)=10*x^4+6*x^1.
The second derivative is: 10*4*x^(41)+6*1*x^(11)=40*x^3+6*x^0.
The second derivative evaluated at x=2 is 40*(2)^3+6*(2)^0=314.
So the method returns 314.
