Consider the curves in the first quadrant that have equations y=Aexp(6x) where A is a positive constant. Different values of A give different curves. The curves form a family, F. Give a formula g(y) for the slope at (xy) of the member of F that goes through (xy). The formula should not involve A or x.

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Consider the curves in the first quadrant that have equations y=Aexp(6x) where A is a positive constant. Different values of A give different curves. The curves form a family, F. Give a formula g(y) for the slope at (xy) of the member of F that goes through (xy). The formula should not involve A or x.

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i am getting g(y)=6y, but i am probably wrong. do you know the answer?
i will write what i did, and you can see if it makes sense. you have to write the slope in terms of y so say (x,y) is on the graph. that means it is \[(x,Ae^{6x})\] and so \[x=\frac{1}{6}\ln(\frac{y}{A})\]
then the derivative of \[Ae^{6x}\] is \[6Ae^{6x}\] replace x by \[\frac{1}{6}\ln(\frac{y}{A})\] and get \[6y\] but i would not bet money on this answer

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it was right thanks! :)

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