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This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.
Statement
Goal
Story:Louise is learning calculus in her maths courses and she likes the idea. When doing her homework, she is not sure and she wants to check her answers with yours. Could you create a program so that we can check the answers?
Calculate, evaluate the partial derivative of a given formula.
For instance,
given the function formula "(5*(x*(y^2)))"
and "y x", the variables in respect with you must derive it
So here f(x,y) = 5xy²
and you have to calculate:
d²f(x,y)
----------
dxdy
it gives you the formula 10*y,
At last "x 2 y 6" means x=2, y=6,
gives you the values with which you must evaluate the obtained derivative
So the answer should be 60
Note:
To simplify the task, only consider
Negative power has no parenthesis.
e.g. (((18*(x^
vars may be in other forms other than x, y, and z. Similar to identifiers in many programming languages, the var would be some letter followed by letters, numbers or underscore.
link about calculus rules: https://en.wikipedia.org/wiki/Differentiation_rules
The rules needed here:
a'=0
(a*x)'=a
(x^a)'=a*x^(a-1) (when a is not 0)
(u+v)'=u'+v'
(u*v)'=u'*v+v'*u
Input
Line 1: formula
Line 2: list of vars for partial derivative, separated by space, length of the list will be 1, 2 or 3.
Line 3: vars' values, paired and separated by space
Line 2: list of vars for partial derivative, separated by space, length of the list will be 1, 2 or 3.
Line 3: vars' values, paired and separated by space
Output
The result (always an integer).
Constraints
All numbers are integers.
Line 2 would give a list from 1 to 3 different/same vars to do partial derivative.
You can assume that the second argument of ^ is constant, to be simple and avoid "ln" or "e^x".
e.g.:
will appear:
(x^y)
x
x 1 y 1
won't appear (this could be too complex):
(x^y)
y
x 1 y 1
Line 2 would give a list from 1 to 3 different/same vars to do partial derivative.
You can assume that the second argument of ^ is constant, to be simple and avoid "ln" or "e^x".
e.g.:
will appear:
(x^y)
x
x 1 y 1
won't appear (this could be too complex):
(x^y)
y
x 1 y 1
Example
Input
(5*(x*y)) x x 2 y 6
Output
30
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