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indie452
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Homework Statement
differentiate (x2)lnx
im having a blonde moment...how do you start?
Cyosis said:can write the part in the exponent slightly easier by using [itex]\ln x^2=2\lnx[/itex].
The formula for differentiating (x^2)^(ln[x]) is d/dx[(x^2)^(ln[x])] = (x^2)^(ln[x]) * (2ln[x] + 1/x).
The rule for differentiating a power raised to another power is d/dx[(f(x))^n] = n(f(x))^(n-1) * f'(x).
Yes, the power rule can be used to differentiate (x^2)^(ln[x]) as it follows the formula d/dx[(f(x))^n] = n(f(x))^(n-1) * f'(x).
The derivative of ln[x] is 1/x.
Yes, the derivative of (x^2)^(ln[x]) is continuous as it follows the rules of differentiation and the function is continuous for all values of x.