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Find the derivative of the function using the definition of a derivative. State the domain of the function and the domain of its derivative.$g(t)=\frac{1}{\sqrt{t}}$

domain of the function $(0, \infty)$domain of the derivative $(0, \infty)$

Calculus 1 / AB

Chapter 3

Derivatives

Section 2

The Derivative as a Function

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Hi, this is Claire. So when number 30 of Stuarts vile calculus books we're gonna find the derivative isn't the definition and state the domain of both the original and derivative wants you. It's already wrote the definition of the derivative and the original function to make things faster. But instead of plugging explicit, each working on actually plucking tea, plus each were just substituting. Um, we're substituting tea instead of Max. So it's going to be G prime of tea calls women. That's H approaches. So is going to be won over screw hump t plus beach subtracted by orginal questions. So one over a square root of team that's all over each. When you simplify that, it becomes a woman, each ghosting squaring off T minus skirt of teeth claws each all over each time square root of T plus two each times squared off T. Then when you simplify that continuously, you're going to get well in each approaches. Sarah and I got a beach over each times square root well, t times t plus slim this more not to play about one time more. One skirt of tea waas t plus beach. When you simplify that you get negative one over. It's clear memory of tee times. T times were tough plus square root of tea. Then that's flies into negative one team, too Negative. Three. House for our domain. For the original equation, it's going to be, um, zero to infinity. We can't we can't use Brock. It's because if we use zero on the bottom is gonna be undefined as well as infinity. Because one over in phonied infinity is zero. And that becomes undefined and the same for our f of prime well, G of crime. Miri. Instance. What? This is g of team and G prime tea and they both have the same dough means, yeah.

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