Subject: Math-Derivatives
Name: kate

What is the derivative of 5 to the 5x-2 at x equals 0.8?

Hi Kate,

Suppose that you call your function y, then

y = 55x - 2

To differentiate y first take the natural log of both sides and use the fact that log(ab) = b log(a). Thus

log(y) = log(55x - 2) = (5x - 2) log(5)

Now differentiate both sides with respect to x to get

(1/y) dy/dx = 5 log(5) or dy/dx = 5y log(5)

To complete the problem, substitute y = 55x - 2 and evaluate when x = 0.8.


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