Differentiate, but do not simplify: f(x)=√3cos(x)-e^-2x

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Start date May 12, 2020
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Differentiate Simplify

In summary, "Differentiate, but do not simplify" means to find the derivative of a function without simplifying it. To differentiate a function, you must use the rules of differentiation, such as the Power Rule, Product Rule, Quotient Rule, and Chain Rule. The purpose of differentiation is to find the rate of change, maximum and minimum values, and concavity of a function. When differentiating a function with multiple terms, you must apply the rules of differentiation to each term and then add them together. To differentiate a function with trigonometric functions, you must use the Chain Rule and remember to apply the derivative rules for each specific trigonometric function.

May 12, 2020

ttpp1124

Homework Statement: can someone check if it's correct?

Relevant Equations: n/a

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May 12, 2020

etotheipi

It's fine, but you can skip the ##u## substitution to do it more quickly.

Related to Differentiate, but do not simplify: f(x)=√3cos(x)-e^-2x

1. What is the purpose of differentiating a function?

Differentiation is a mathematical process that allows us to find the rate of change of a function. It helps us understand how the output of a function changes with respect to its input.

2. How do you differentiate a function?

To differentiate a function, we use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules allow us to find the derivative of a function, which represents its rate of change.

3. Why is it important to not simplify a differentiated function?

Simplifying a differentiated function can lead to a loss of information and may not accurately represent the original function. By not simplifying, we can better understand the behavior and properties of the function.

4. What does the function f(x) = √3cos(x) - e^-2x represent?

This function represents a combination of a cosine function and an exponential function. The square root of 3 in front of the cosine function indicates a vertical stretch, while the negative exponent in the exponential function indicates a decay.

5. What is the significance of the negative sign in front of e^-2x?

The negative sign indicates that the exponential function is decaying, meaning it approaches 0 as x increases. This is in contrast to a positive sign, which would indicate exponential growth as x increases.