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lilg132
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\[M = 4.2e ^{2x} - 2.9e ^{-0.2x}\]
mathdood
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okay well what is the derivative of e^x?
lilg132
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xe? i dont know
mathdood
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it is e^x*x' and the derivative of x is 1 so you have e^x but in this case since you have 2x and -0.2x you need to bring those down and differentiate you know what I mean?
mathdood
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crazy eh derivative of e^x is e^x!!
lilg132
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LOL
lilg132
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no i dont explain further please :(
mathdood
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but that it isn't the end of your problem okay do you know how to take simple derivative like x^2? like do you know the power rule?
lilg132
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x^2 would be 2x?
mathdood
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right just making sure.
mathdood
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Okay so when you see e^x you have e^x and when you see e^2x you get e^2x*(2x)' the ' means derivative. You understand? If not I don't mind continuing at all.
lilg132
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ok.. e^2x * (2x)' is e^2x
mathdood
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no what is the derivative of 2x?
lilg132
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x^2 ?
lilg132
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mindboggling
mathdood
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no that is the integral of 2x think about it like this. The derivative is the rate of change of the function so you are looking for the how fast the function is changing. so how fast is 2x changing?
mathdood
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sorry not how fast but by how much is it changing for each value of x
lilg132
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2?
lilg132
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by 2?
mathdood
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yes =) just for fun what is the derivative of 2?
lilg132
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LOL erm not sure
lilg132
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1?
lilg132
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wait
its a constant
lilg132
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so 0
mathdood
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sorry I know I am dragging this out I just want to help you understand. Well think how much is the function y=2 changing over time right!! =)
mathdood
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mathdood
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Anyway back to the problem
lilg132
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ok :)
mathdood
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so if (e^2x)' = 2e^2x then what do you think (4.2e^2x)' = ?
lilg132
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8.4e^2x
lilg132
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please be right
mathdood
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good stuff dude now how about (−2.9e^(−0.2x))' = ?
mathdood
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yes you got it =) keep going you can do this
lilg132
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:D 0.58e^-0.2x?
mathdood
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I didn't check on the calculator but it looks right dude so now you just have to put the whole thing together you want to show me what that looks like?
lilg132
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ok one second :D
lilg132
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dm/dx = 8.4e^2x + 0.58e^-0.2x
mathdood
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awesome dude high five! =)
lilg132
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woooooooooooo !!!
lilg132
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thanks alot mate appreciate it
mathdood
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not a problem =) thanks