7-3-57 derivative of a constant to a variable power
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When finding the derivative of Y equal 4 to the square root of
T1, method to do this is to think about Y equal E to the
lane of four square roots of T.
That square root of T therefore is in the exponent and can be
brought down.
So we get E square root of TLN 4.
Remember, LN4 is a constant, so when we want to find DYDT, we're
going to take the derivative of E to something which is E to
that something times the derivative of that exponent or
that square to TLN four.
Well, we know that E squared to TLN 4 is really just the same
thing as 4 sqrt t because we rewrote that as an equivalent.
So now all we have to do is find the derivative of the square to
TLN 4.
Square to T is 1 / 2 square root of TLN of four LN4 we could
think of as 2 ^2.
And then this two in the exponent could come down in
front and cancel with the two down in that denominator.
So we'd have 4 square roots of T 1 / sqrt t lane 2 as a great
final answer.