Question

Find the derivative of the function:
y=6e^-x + e^5x

Answer 1

\[y \prime = -6e^-x +5e ^{5x}\]

Answer 2

First, remember that the derivative of e^x is just e^x. Next remember that chain rule:

y' = -6e^-x + 5e^5x

Answer 3

e^-x sorry.

Answer 4

Can you give me some steps, so I know where I should go.

Answer 5

y = 6e^-x + e^5x

First lets evaluate the derivative of each term:

For the derivative of 6e^-x:
the derivative keeps the coefficient 6. Next we take the derivative of the outside function (e^-x) which is just itself: e^-x. Next we notice that -x is a function itself, so use the chain rule to take the derivative of -x, which is -1, and multiply it with everything else. Remember that the Chain Rule states that the derivative of f(g(x)) = f'(g(x))*g'(x) Therefore:

d/dx (6e^-x) = 6*e^-x*-1, where 6 is the coefficient, e^-x is the derivative of the outside function e^-x, and -1 is the derivative of the inside function -x.

Answer 6

Now we do the same thing for the next term: e^5x

The derivative of e^5x is just itself: e^5x. Next we have to apply the chain rule to the inside function: 5x. The derivative of 5x is 5 so we get:

d/dx (e^5x) = (e^5x)*5 = 5e^5x

So now we just combine the two terms together to get:

y' = -6e^-x + 5e^5x

Answer 7

Oh, dang...I got it. Thanks!
That was so so easy and I couldn't figure it out.