Is This Solution for a Calculus Problem Correct?

In summary, "Differentiating" means finding the derivative of a function, which involves finding the rate of change of the function at a specific point. To differentiate a function, you need to use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. The purpose of differentiation is to determine the rate of change of a function, find maximum and minimum values, and solve optimization problems. Any type of function can be differentiated as long as it is continuous and differentiable. Differentiation is the inverse operation of integration, which involves finding the antiderivative of a function to find the area under the curve.
  • #1
ku1005
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Hey Guys, this is one of the Q's in my book which I have completed but would just like to check whether (a) it is correct and B whether I can leave it in this format for the answer?

cheers

I used the fundamental theorem part 1 and the chain rule due to upper limit of integration being x^3. I posted as attachements as my text wouldn't work in here.thanks heaps!

rhys
 

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  • #2
I can't see your picture unfortunately.
 

What does it mean to "Differentiate the Following"?

Differentiating means finding the derivative of a function. This involves finding the rate of change of the function at a specific point, also known as the slope of the tangent line.

How do I differentiate a function?

To differentiate a function, you need to use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the derivative of a function step by step.

What is the purpose of differentiation?

Differentiation is used to determine the rate of change of a function. It is also used to find the maximum and minimum values of a function, as well as to solve optimization problems in mathematics and science.

Can I differentiate any type of function?

Yes, you can differentiate any type of function as long as it is continuous and differentiable. This means that the function must have a defined slope at every point on its graph.

What is the difference between differentiation and integration?

Differentiation and integration are inverse operations of each other. Differentiation involves finding the derivative of a function, while integration involves finding the antiderivative of a function. In other words, differentiation finds the slope of a function, while integration finds the area under the curve of a function.

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