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Find the first and second derivatives of the function.$ f(x) = 0.001x^5 - 0.02x^3 $

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$$f^{\prime \prime}(x)=0.02 x^{3}-0.12 x$$

00:32

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

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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.

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.

01:01

Find the first and second …

01:10

02:09

Find the second derivative…

01:35

01:25

Find the first, second, an…

he had square. So when you read here, so we're gonna find the first and second derivative. So starting off with the first derivative, we have d over D X 0.1 next to the fifth, minus 0.2 x to the third. This is equal to We use the constant multiple rule to take out the Constance and apply the power when we get 0.1 times five x to the five minus one. Power minus point in syrup too. Three x do the three minus one power and this becomes equal to 0.5 x to the fourth power minus 0.6 Next to the second power. The second derivative, we have d over DX of our first derivative 0.5 x to the fourth power minus 0.6 hex to the second power right here we could erase a sorrow. These are some indifference rule in our constant multiple roll and we get point 005 d over d x where x to the fourth, minus 0.6 d over d x X square and leaves the power rule to get point 02 x to the third minus point 12 x

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