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If $ f(2) = 10 $ and $ f'(x) = x^2 f(x) $ for all x, find $ f''(2). $

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00:44

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

Baylor University

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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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it's clear. So name read here. So we're gonna use our product rule. Then we get us The drug builder of it is is equal to two x of X plus X squared times, the derivative of the We know that the derivative of off to is equal to two square time's up of two, which is equal to four times 10 which gives us 40. So when we plug it in to our equation here we get the second derivative of up of two is equal to two times two times 10 plus two square plus 40 which is equal to 200.

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