Question 1028454: Using logarithmic differentiation, find the derivative of F(x) = (x^2+5)^(cot2x). Write the derivative in terms of x. Found 2 solutions by stanbon, robertb:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Using logarithmic differentiation, find the derivative of
F(x) = (x^2+5)^(cot2x). Write the derivative in terms of x.
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Rewrite::
y = (x^2+5)^(cot(2x))
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Take the log of both sides::
let y = (cot(2x))*log(x^2+5)
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Take the derivative of both sides::
y'/y = (cot(2x))(2x) + (x^2+5)(-2csc^2(2x))
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y' = [(x^2+5)^cot(2x)][cot(2x)(2x)-4(x^2+5)(csc^2(2x)]
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Cheers,
Stan H.
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