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2 cards from this section. Quick, good the night before a test.
What is the derivative of f(x) = e^x?
Refer to the specific property of e.
Calculate the derivative of f(x) = 2^x.
Remember to multiply by ln(base).
What is the derivative of f(x) = e^x?
Think about how e behaves under differentiation.
For what base does f(x) = a^x have a derivative formula of f'(x) = a^x ln(a)?
Recall the derivative formula for constants.
If a turtle population grows exponentially, represented by P(t) = P0 e^(kt), where k is a constant. If at t = 0, P0 = 1000 and k = 0.03, find the population after 5 years.
Remember the formula for population growth!
Given the function f(x) = 3^x, find an x-value such that the slope of the tangent line at that point equals 20.
You will have to use logarithms to isolate x.
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