log5(x^2-1)^(1/2)

Can you differentiate this equation for me
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1 Answer

Let y=log₅√(x²-1). 5^y=√(x²-1), 5^(2y)=x²-1, e^(2yln(5))=x²-1.

Differentiate wrt x:

2ln(5)e^(2yln(5))(dy/dx)=2x, 2ln(5)(x²-1)(dy/dx)=2x,

dy/dx=x/(ln(5)(x²-1)), so derivative is x/(ln(5)(x²-1)).

by Top Rated User (1.1m points)

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