f'(xⁿ)
To find the derivative of f(xⁿ), let’s use the power rule of differentiation
To find the derivative of f(xⁿ), let’s use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = uⁿ, where u is a differentiable function of x and n is a constant, then its derivative with respect to x is given by:
f'(x) = n*u^(n-1)*u’
In this case, f(x) = xⁿ, where n is a constant and x is the variable. Therefore, u = x and n = n.
Now, let’s find the derivative f'(x) using the power rule:
f'(x) = n*x^(n-1)*u’
In this case, u’ = 1, since the derivative of x with respect to x is 1.
Therefore, the derivative of f(xⁿ) is given by:
f'(x) = n*x^(n-1)*1
Which simplifies to:
f'(x) = n*x^(n-1)
So, the derivative of f(xⁿ) is n times x to the power of n minus one.
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