Find All The Possible Functions With The Derivative:
f'(x) = cos(x) - 2e^(2x) + 5
Can someone explain this question to me?
f'(x) = cos(x) - 2e^(2x) + 5
Can someone explain this question to me?
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You want to find all functions f such that f' is the given function. There is more than one, and they just differ by a constant. When you take the derivative, the constant term drops out, since the derivative of a constant is 0.
Just integrate each term separately, and add a constant term.
The answer is:
f(x) = sin(x) - e^(2x) + 5x + c
The constant c can be any number.
Just integrate each term separately, and add a constant term.
The answer is:
f(x) = sin(x) - e^(2x) + 5x + c
The constant c can be any number.