7/sqrt(t) |

State the domain of the function. (Enter your answer using interval notation.)

State the domain of its derivative. (Enter your answer using interval notation.)

Hello Brandon, any time you see a division sign or times sign when thinking of differentiation, first you think of converting somehow to get rid of the division or times sign. In this case the definition of derivative formula is always in x so you need to think maybe of changing the variables. t to x’s so: f(x) = 7/√(x), next since the numerator is only a constant this is not a quotient rule problem, however I realize that you are told to use the definition of derivative to get the answer. You still need to convert before you try that, so: f(x) = 7*x^(-1/2). To find the derivative you’d take the exponent (-1/2) and multiply it times what ever’s in front of the x in this case 7 to get -7/2, then take 1 away from the exponent -1/2 or: -1/2 – 2/2 = -3/2 this will give you -7/2*x^(-3/2), then convert to -7/2/x^(3/2). Now as far as my programs go I haven’t programmed that because I don’t think it would appear on any test. If it did everyone would flunk it probably. Let me know what you think, Tom

## Leave a Reply