# Calc

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Find f'(7) for f(x)=6x^ln(x)

• Calc -

Use chain rule.
Let
y=6xln(x)
take log on both sides:
ln(y) = ln(6)+ln(x)*ln(x)
ln(y) = ln(6) + ln²(x)
differentiate both sides w.r.t. x
(1/y)y' = 0 + 2ln(x)*(1/x)
y' = dy/dx
= y*2ln(x)*(1/x)
= 6xln(x)*2ln(x)*(1/x)
= 12xln(x)-1*ln(x)

Check my calculations.

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