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Find the derivative of the function.$ f(x) = \sqrt{5x + 1} $

$=\frac{5}{2 \sqrt{5 x+1}}$

00:22

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

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let's find the derivative of this function. And since it's a composite function with one function inside another, we're going to use the chain rule, and I like to rewrite it when I have a square root. I like to write it as five x plus one to the 1/2 power and use the power rule. So we start the chain ruled by taking the derivative of the, uh, the outside function. So we get 1/2 times five x plus one to the negative 1/2. Okay, we bring down the old power and we subtract one to get the new power. Now we multiply by the derivative of the inside, and that would be the derivative of five X plus one. And that would just be five. So we have our derivative, and now we're going to simplify. So what we can do is multiply the five and 1/2 and that's five halves. We can leave the five on the top and put the two in the denominator. And then because we have a negative exponents, we're gonna move that term to the denominator as well. So we have five x plus one to the 1/2 in our denominator. Now let's go ahead and change our notation back to radical notation. So we have 5/2 times a square root of five x plus one.

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