# Derivative of exponents question HELP

## Homework Statement

find the derivative of: 4e^t((e^2t)-(e^t))

## Homework Equations

d/dx[b^x] = lnb(b^x)d/dx(x)

## The Attempt at a Solution

I tried subtracting the two exponents in the brackets as well as multiplying it out. both wrong. Help?

$$4e^{t}(e^{2t}-e^{t})$$ ?

You should make it easier on yourself and distribute that $4e^{t}$ through the parenthesis and then take the derivative. Remember to use the chainrule, for example, recall that:
$$\frac{d}{dx}e^{f(x)}=e^{f(x)}\frac{df(x)}{dx}$$

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## Homework Statement

find the derivative of: 4e^t((e^2t)-(e^t))

## Homework Equations

d/dx[b^x] = lnb(b^x)d/dx(x)

## The Attempt at a Solution

I tried subtracting the two exponents in the brackets as well as multiplying it out. both wrong. Help?

So just to be clear, you are trying to find

$$\frac{d}{dt}\left(4e^t\left(e^{2t}-e^t\right)\right)$$

Correct?

I tried subtracting the two exponents in the brackets

$$e^{2t}-e^t\neq e^t$$

if that's what you were implying. Remember the rules for subtracting indices are

$$\frac{a^b}{a^c}=a^{b-c}$$

When you multiplied the factor out (expanded) what did you get?