Differentiate, but do not simplify: f(x)=sin(cos(x^2))

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Start date May 12, 2020
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Differentiate Simplify

In summary, differentiation is a mathematical process used to find the rate of change of a function by calculating the slope of the tangent line at a specific point on the function's graph. To differentiate a function, one must use the rules of differentiation, which involve taking the derivative of each term and simplifying the resulting expression. It is important not to simplify when differentiating because it can change the function's behavior and make it harder to analyze. When differentiating a function with multiple layers, the chain rule is used. As long as a function is continuous and differentiable, it can be differentiated using various techniques.

May 12, 2020

ttpp1124

Homework Statement: can someone see if my work is correct?

Relevant Equations: n/a

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May 12, 2020

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ttpp1124 said:

Homework Statement:: can someone see if my work is correct?
Relevant Equations:: n/a

View attachment 262672

It is correct.

May 12, 2020

robphy

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https://www.desmos.com/calculator/dtnoujdur3

1. What does it mean to differentiate a function?

Differentiation is a mathematical process that calculates the rate of change of a function with respect to its independent variable. It essentially gives us the slope of the function at any given point.

2. Why is it important to differentiate a function?

Differentiation is important because it allows us to analyze the behavior of a function and make predictions about its values at different points. It also helps us find the maximum and minimum points of a function, which is useful in optimization problems.

3. How do you differentiate a composite function?

To differentiate a composite function, such as f(x)=sin(cos(x^2)), we use the chain rule. This involves taking the derivative of the outer function and multiplying it by the derivative of the inner function.

4. What is the difference between differentiation and simplification?

Differentiation and simplification are two different mathematical processes. Differentiation involves finding the rate of change of a function, while simplification involves reducing a complex expression to its simplest form. In the given function, we are asked to differentiate it without simplifying it, meaning we do not need to simplify the expression after differentiating.

5. Can you differentiate a function with more than one variable?

Yes, it is possible to differentiate a function with more than one variable. This is known as partial differentiation, where we take the derivative with respect to one variable while holding the other variables constant. However, in the given function f(x)=sin(cos(x^2)), there is only one variable, x, so we do not need to use partial differentiation.