๐/๐๐ฅ[๐ฅ^๐]
The derivative of ๐ฅ raised to the power ๐, denoted by ๐/๐๐ฅ[๐ฅ^๐], can be found using the power rule of differentiation. The p
The derivative of ๐ฅ raised to the power ๐, denoted by ๐/๐๐ฅ[๐ฅ^๐], can be found using the power rule of differentiation. The power rule states that when differentiating a variable raised to a constant power, you multiply the variable by the constant power, and then decrease the power by 1.
In this case, since ๐ฅ^๐ has ๐ as the exponent, the power rule tells us that the derivative of ๐ฅ^๐ is ๐ times ๐ฅ^(๐-1).
๐/๐๐ฅ[๐ฅ^๐] = ๐๐ฅ^(๐-1)
Here, the derivative ๐/๐๐ฅ[๐ฅ^๐] represents how the function ๐ฅ^๐ changes as ๐ฅ changes.
For example, if we have the function ๐(๐ฅ) = ๐ฅ^3, we can find its derivative by applying the power rule. The exponent here is 3, so we multiply 3 by ๐ฅ^(3-1) which simplifies to ๐ฅ^2.
๐/๐๐ฅ[๐ฅ^3] = 3๐ฅ^2
The derivative of ๐ฅ^3 is 3๐ฅ^2. This means that as ๐ฅ changes, the rate of change of ๐ฅ^3 is 3 times ๐ฅ^2.
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