Differentiate and simplify: f(x) = x^2(2^-3x)

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Start date May 12, 2020
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Differentiate Simplify

In summary, differentiating a function involves finding its derivative, while simplifying a function involves reducing it to its simplest form. To differentiate a function, you can use the power rule and the chain rule. Simplifying a function means combining like terms and using mathematical rules. We differentiate and simplify functions to better understand their behavior and make calculations easier. While most functions can be differentiated and simplified, some may require advanced techniques and may not have a simple derivative.

May 12, 2020

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Homework Statement: Can someone check to see if it's simplified fully?

Relevant Equations: n/a

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May 12, 2020

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Related to Differentiate and simplify: f(x) = x^2(2^-3x)

What is the function f(x)?

The function f(x) is defined as f(x) = x^2(2^-3x).

What does the term "differentiate" mean in this context?

In calculus, differentiation is the process of finding the rate of change of a function with respect to its independent variable. In simpler terms, it is the process of finding the slope of the function at a given point.

How do you differentiate the function f(x) = x^2(2^-3x)?

To differentiate this function, we use the power rule and the chain rule. First, we bring down the exponent 2 and multiply it by the coefficient 2^-3x, giving us 2x(2^-3x). Then, using the chain rule, we multiply by the derivative of the exponent, which is -3x(2^-3x). Combining these two terms, we get the final derivative of f(x) = -3x^2(2^-3x).

What does it mean to "simplify" a function?

Simplifying a function means to manipulate the expression in a way that makes it easier to understand or work with. This can involve factoring, combining like terms, or using other algebraic techniques to simplify the expression.

How do you simplify the function f(x) = -3x^2(2^-3x)?

To simplify this function, we can first factor out a common term of 2^-3x, giving us f(x) = -3x^2(2^-3x). Then, using the rule for negative exponents, we can rewrite 2^-3x as 1/2^3x. Combining this with the remaining term, we get the simplified function f(x) = -3x^2/2^3x.