I need help differentiating this question:
3e^-4x
that's three e to the power of negative 4x.
when you differentiate, you get:
-12e^-4x
thanks, but how come it's not -12e^-4x-1, or do i just not minus a one when the power is a co-efficient?
Remember, the differential of e^x is also e^x. So, the final answer is e^xdx. That is, you just differentiate what's in the exponent. In your case, the differential of what's in the exponent is -4, so the final answer is just -4 x the original, or -4 x (3e^-4x).
To differentiate the expression 3e^(-4x), you can follow these steps:
1. Recognize that e^(-4x) is the exponentiated form of a constant, where the base is Euler's number, e, raised to the power of -4x.
2. Differentiate e^(-4x) by applying the chain rule. The chain rule states that the derivative of f(g(x)) is given by f'(g(x)) * g'(x), where f(x) represents the outer function and g(x) represents the inner function.
3. In this case, the outer function is e^x, which has a derivative equal to itself, so its derivative is e^x.
4. The inner function is -4x, which has a derivative of -4.
5. Apply the chain rule by multiplying the derivative of the outer function (e^x) by the derivative of the inner function (-4). This gives you: e^x * (-4) = -4e^x.
6. Multiply the result from step 5 by the coefficient 3 in front of e^(-4x) in the original expression: -4e^x * 3 = -12e^x.
Therefore, the derivative of 3e^(-4x) is -12e^(-4x), and there is no need to subtract 1 from the exponent.