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

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

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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### Video Transcript

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

#### Topics

Derivatives

Differentiation

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp