How do you use logarithmic differentiation to find the derivative of #y=(tanx)^(1/x)#?
By signing up, you agree to our Terms of Service and Privacy Policy
To use logarithmic differentiation to find the derivative of ( y = (\tan x)^{\frac{1}{x}} ), you would follow these steps:

Take the natural logarithm of both sides: ( \ln y = \ln \left( (\tan x)^{\frac{1}{x}} \right) ).

Apply the logarithm property ( \ln(a^b) = b \ln(a) ) to simplify: ( \ln y = \frac{1}{x} \cdot \ln(\tan x) ).

Differentiate both sides with respect to ( x ) implicitly: ( \frac{1}{y} \cdot \frac{dy}{dx} = \frac{1}{x^2} \cdot \ln(\tan x) + \frac{1}{x} \cdot \sec^2 x ).

Solve for ( \frac{dy}{dx} ): ( \frac{dy}{dx} = y \left( \frac{1}{x^2} \cdot \ln(\tan x) + \frac{1}{x} \cdot \sec^2 x \right) ).

Substitute back ( y = (\tan x)^{\frac{1}{x}} ): ( \frac{dy}{dx} = (\tan x)^{\frac{1}{x}} \left( \frac{1}{x^2} \cdot \ln(\tan x) + \frac{1}{x} \cdot \sec^2 x \right) ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7