Finding Derivative of y=5^(3-3x)

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In summary, a derivative is a mathematical concept that measures the rate of change of a function. This can be found using the process of differentiation, which involves applying specific rules and formulas to simplify the result. One commonly used rule is the power rule, which states that the derivative of a function raised to a power is equal to the power multiplied by the original function raised to the power minus one. Other rules and methods for finding derivatives include the product rule, quotient rule, chain rule, and using limits. It is important to be familiar with these techniques in order to find derivatives accurately and efficiently.
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chantella28
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Hey guys,
I have a calculus problem that should be easy but I haven't taken calc in a few years so I can't remember where to begin. If somebody could give me some help with this, that would be great

find the following derivative: y=5^(3-3x)
 
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  • #2
You know the derivative of e^x and the chain rule (right?), so just use these along with the fact that:

[tex]5^{a}=e^{a \ln 5} [/tex]
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a given point. It measures how much a function changes in response to small changes in its input variable.

How do you find the derivative of a function?

To find the derivative of a function, you can use the process of differentiation. This involves using specific rules and formulas to find the derivative of each term in the function and then simplifying the result.

Can you explain the power rule for finding derivatives?

The power rule is a commonly used rule for finding derivatives. It states that the derivative of a function raised to a power is equal to the power multiplied by the original function raised to the power minus one. In other words, if the function is y = x^n, then the derivative is y' = nx^(n-1).

How do you apply the power rule to find the derivative of y=5^(3-3x)?

To apply the power rule to this function, you first need to rewrite it in the form y = (5^3)(5^-3x). Then, using the power rule, you can find the derivative as y' = 0 + (5^-3x)(ln5)(-3) = -3ln5(5^-3x).

Are there any other rules or methods for finding derivatives?

Yes, there are several other rules and methods for finding derivatives, such as the product rule, quotient rule, and chain rule. Additionally, you can also use the concept of limits to find derivatives. It is important to understand and be familiar with these different techniques in order to find derivatives accurately and efficiently.

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