Question

Find the derivative of f(y)=9tan(y)-\sqrt{y}/4-10/y^5\sqrt{y}[/tex]

Answer 1

f'(y) =
`9sec^2(y)-(1)/(8√(y) ) - (5y^5√(y) - 50y^4√(y) )/(y^(10))` or any equivalent form

Explanation:

rewriting the equation to contain only exponents no roots

`f(y)= 9tan(y)-(1)/(4) y^(1)/(2) -(10y^(1)/(2))/(y^5)`

using power rule, quotient rule, and trig derivatives

f'(y) =
`9sec^2(y)-(1)/(8√(y) ) - ((5y)/(√(y))(y^5) - 5y^4(10y^(1)/(2)) )/(y^(10))`

f'(y) =
`9sec^2(y)-(1)/(8√(y) ) - (5y^5√(y) - 50y^4√(y) )/(y^(10))`