Find the derivative of the function : y = 5^-1/x

Question

Find the derivative of the function : y = 5^-1/x

 

I know I need to apply the Chain Rule:

d/dx 5 (-1/x) * d/dx (-1/x)

 

However, doesn't d/dx 5 (-1/x) become 0 * (-1/x)?

 

 

#25, p205

ANSWER:      y' = 5^-1/x (ln5)/x²

Answer 1

Natural log both sides of equation.

 

ln(y) = ln(5^-1/x)

 

 

ln(y) = (-x^-1)ln(5)

 

 

Use implicit differentiation.

 

(1 / y)y' = x^-2ln(5)

 

 

y' = y(x^-2ln(5))

 

 

Substitute the value of y into the derivative.

 

y' = (5^-1/x)(x^-2ln(5))