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Find $f^{\prime}(x)$ if $f(x)=\frac{2 x+3}{3 x-2}$

$-13 /(3 x-2)^{2}$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 5

Derivative Rules 2

Derivatives

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Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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Find $f(3 x)$ if $f(x)=4-2…

our task is to find the derivative of this quotient and this is called a quotient. Giant division problems. Which is why we're going to do the quotient rule. Eso What's the questionable? That's taking the derivative of the top. So f prime is equal to the derivative of the top is just too. You leave the bottom alone and then it's minus the derivative of the bottom, which is just three because the derivative of three x three, the derivative of negative zero sorry of native to the constant is zero. Do you leave the top alone? Yeah, all over the denominator square. Now, some teachers will let you leave your answer like this also, I'll circle this because some teachers Yeah, this is good enough. Other teachers, though, will require that you distribute in and so just a little scratch work under the scratch Working blue, you'll see that you have six X minus four and the minus six X minus nine and then you can see that these exes will cancel. So what will be left with this negative 13 Negative for minus nine over Oh, 67 three X minus two squared. There you go.

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