Question 999361
Very confused on taking antiderivatives. In my class I am not allowed to use integrals, just math logical to solve this problem: e^(x/5) + sin(3x). I know it's sort of like figuring out what the function must have been before the derivative was taken but this keeps giving me trouble. I have to reverse the derivative and get it back to its original state. sin(3x) is simple enough for it to be +sin(3x) it must be a negative cosine and something for which cancels the 3 out so 1/3 therefore, -1/3cos(3x) would be the original. But the original of e^(x/5) this one baffles me. It's really the (x/5) that I don't get. How does undoing that work exactly? what must I do/understand first before getting its antiderivative/
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d/dx(e^x) = e^x
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d/dx(e^(ax)) = a*e^(ax)