## Finding the derivative of m(x)=-e^xcosx

1. The problem statement, all variables and given/known data

Find the derivative of m(x)=-e^x*cosx at x=1 graphically and algebraically.

2. Relevant equations

3. The attempt at a solution

So first i just attempted to find the derivative:

m'(x)=-xe^(x-1)*(-sinx)----> is this correct?

so to find at x=1 i just sub in 1.

m'(1)=-(1)e^(1-1)*(-sin1)
m'(1)=-1e^0*(-sin1)
m'(1)=0.01745

Is this correct? When i tried graphing the derivative i got a different answer so it made me second guess my original answer.

Any help is very much appreciated, thank you.
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 Quote by Buzzlastyear 1. The problem statement, all variables and given/known data Find the derivative of m(x)=-e^x*cosx at x=1 graphically and algebraically. 2. Relevant equations 3. The attempt at a solution So first i just attempted to find the derivative: m'(x)=-xe^(x-1)*(-sinx)----> is this correct?
No, it's not. You are mis-using some basic properties of the derivative. In the first place the "product rule": the derivative of fg is (fg)'= f'g+ fg', not just " f'g' " as you have here.

Second, the rule " (xn)'= n xn-1" applies only when the variable is the base and the exponent is a constant. With ex or, more generally, ax, for any positive a, that rule does not apply. Look up the derivative of ex sdecifically.

 so to find at x=1 i just sub in 1. m'(1)=-(1)e^(1-1)*(-sin1) m'(1)=-1e^0*(-sin1) m'(1)=0.01745 Is this correct? When i tried graphing the derivative i got a different answer so it made me second guess my original answer. Any help is very much appreciated, thank you.
 Okay, thank you. I had not learned about the derivative of exponential functions but looked it up. So is -e^x still just -e^x?

## Finding the derivative of m(x)=-e^xcosx

And as for using the product rule, would this be correct?

m'(x)=-e^x*(cosx) + (-sinx)(-e^x)

assuming my previous post is correct?
 Recognitions: Gold Member Science Advisor Staff Emeritus Yes, f(x)= ex has the very nice property that its derivative is just f'(x)= ex again. That's why the number "e" has a special symbol.
 Okay, thanks very much for your help.

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