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

Mathematics

1 answer:

MakcuM [25]3 years ago

6 0

Answer:

f'(y) = $9sec^2(y)-\frac{1}{8\sqrt{y} } - \frac{5y^5\sqrt{y} - 50y^4\sqrt{y} }{y^{10}}$ or any equivalent form

Step-by-step explanation:

rewriting the equation to contain only exponents no roots

$f(y)= 9tan(y)-\frac{1}{4} y^\frac{1}{2} -\frac{10y^\frac{1}{2}}{y^5}$

using power rule, quotient rule, and trig derivatives

f'(y) = $9sec^2(y)-\frac{1}{8\sqrt{y} } - \frac{\frac{5y}{\sqrt{y}}(y^5) - 5y^4(10y^\frac{1}{2}) }{y^{10}}$

f'(y) = $9sec^2(y)-\frac{1}{8\sqrt{y} } - \frac{5y^5\sqrt{y} - 50y^4\sqrt{y} }{y^{10}}$

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