Differentiate, but do not simplify: 5^xx^5

In summary, differentiating a function means finding its derivative, or the rate of change of the function. "Not simplifying" in this context means leaving the function in its original form without combining or simplifying any terms. To differentiate a function with exponents, the power rule can be used. This states that the derivative of x^n is nx^(n-1). Differentiation is useful for finding the rate of change of a function and leaving the function in its original form without simplifying allows for a more accurate representation. The use of 5^xx^5 is arbitrary and could be any function with exponents, but it serves to demonstrate the concept of differentiating without simplifying. An example of differentiating without simplifying would
  • #1
ttpp1124
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Homework Statement
I came up with two answers, but are they technically the same just written differently?
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  • #2
Looks right.
 

1. What does it mean to differentiate?

Differentiation is a mathematical process that involves finding the rate of change of a function with respect to its independent variable. It is used to determine the slope or gradient of a curve at a specific point.

2. How is differentiation different from simplification?

Differentiation and simplification are two distinct mathematical processes. Differentiation involves finding the rate of change of a function, while simplification involves reducing a mathematical expression to its simplest form.

3. What does "5^xx^5" mean?

The notation "5^xx^5" means that the function is the product of two variables, 5^x and x^5. In other words, the function is equal to 5 to the power of x, multiplied by x to the power of 5.

4. Why is it important to differentiate without simplifying?

Differentiating without simplifying allows us to find the exact rate of change of a function at a specific point, without losing any information. Simplifying a function may result in a loss of precision and accuracy.

5. How do you differentiate "5^xx^5"?

To differentiate "5^xx^5", we use the power rule, which states that the derivative of x^n is equal to n*x^(n-1). Applying this rule, we get the derivative of "5^xx^5" to be 5^x * (x^5 * ln(5) + 5 * x^4).

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