What is the derivative of (sec(y))/(y^2) ?

The derivative of (sec(y))/(y^2) is (sec(y)(ytan(y)-2))/(y^3)

What is the first derivative of (sec(y))/(y^2) ?

The first derivative of (sec(y))/(y^2) is (sec(y)(ytan(y)-2))/(y^3)

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derivative of

\frac{sec ( y )}{y ^{2}}

\frac{sec ( y ) ( y tan ( y ) - 2 )}{y ^{3}}

Solution steps

\frac{d}{d y} (\frac{sec ( y )}{y ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d y} ( sec ( y ) ) y ^{2} - \frac{d}{d y} ( y ^{2} ) sec ( y )}{( y ^{2} ) ^{2}}

\frac{d}{d y} (sec (y)) = sec (y) tan (y)

\frac{d}{d y} (y^{2}) = 2 y

= \frac{sec ( y ) tan ( y ) y ^{2} - 2 y sec ( y )}{( y ^{2} ) ^{2}}

Simplify

\frac{sec ( y ) tan ( y ) y ^{2} - 2 y sec ( y )}{( y ^{2} ) ^{2}} : \frac{sec ( y ) ( y tan ( y ) - 2 )}{y ^{3}}

= \frac{sec ( y ) ( y tan ( y ) - 2 )}{y ^{3}}

\frac{d}{d t} (5 t^{3} - 10 t)

4^{x} + 1

\frac{d}{d a} (\frac{a ^{2} - 2 a + a}{9})

y^{2} x + 5 x y^{3} + 10 y^{2} + 8 x y

\frac{d}{d a} (\frac{( cos ( a ) )}{( 1 - sin ( a ) )})

What is the derivative of (sec(y))/(y^2) ?
The derivative of (sec(y))/(y^2) is (sec(y)(ytan(y)-2))/(y^3)
What is the first derivative of (sec(y))/(y^2) ?
The first derivative of (sec(y))/(y^2) is (sec(y)(ytan(y)-2))/(y^3)