Find Derivatives of f(x): 60x^2 - 15x^4 & 120x-60x^3

• mimitka
In summary, the function f(x) in this problem is 60x^2 - 15x^4 & 120x-60x^3. The purpose of finding the derivatives of this function is to determine the rate of change of the function at any given point, which can be useful in various scientific and mathematical applications. The steps to find the derivatives of this function are to use the power rule and add the resulting derivatives together. The derivatives of 60x^2 - 15x^4 & 120x-60x^3 are 120x - 60x^3 and 120 - 60x^2 respectively. Finding the derivatives of this function can be applied in real life in various fields
mimitka
f(x)=20x^3 - 3x^5

f '(x)=60x^2 - 15x^4

f ''(x)=120x-60x^3

Is this correct?

Looks like it.

What is the function f(x) in this problem?

The function f(x) is 60x^2 - 15x^4 & 120x-60x^3.

What is the purpose of finding the derivatives of this function?

The purpose of finding the derivatives of this function is to determine the rate of change of the function at any given point. This can be useful in various scientific and mathematical applications, such as optimization problems and calculating velocity or acceleration.

What are the steps to find the derivatives of this function?

The steps to find the derivatives of this function are:

1. Use the power rule to find the derivative of each term in the function.
2. Add the resulting derivatives together to get the overall derivative of the function.

What are the derivatives of 60x^2 - 15x^4 & 120x-60x^3?

The derivatives of 60x^2 - 15x^4 & 120x-60x^3 are 120x - 60x^3 and 120 - 60x^2 respectively.

How can finding the derivatives of this function be applied in real life?

Finding the derivatives of this function can be applied in real life in various fields such as engineering, physics, and economics. For example, in economics, derivatives can be used to determine the marginal cost and marginal revenue of a product, which can help a company make decisions about production and pricing. In physics, derivatives can be used to calculate the velocity and acceleration of an object at a specific point in time. In engineering, derivatives can be used to optimize designs and improve efficiency.

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