What is the derivative of (sec(y))/(y^8) ?

The derivative of (sec(y))/(y^8) is (sec(y)(ytan(y)-8))/(y^9)

What is the first derivative of (sec(y))/(y^8) ?

The first derivative of (sec(y))/(y^8) is (sec(y)(ytan(y)-8))/(y^9)

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derivative of

\frac{sec ( y )}{y ^{8}}

\frac{sec ( y ) ( y tan ( y ) - 8 )}{y ^{9}}

Solution steps

\frac{d}{d y} (\frac{sec ( y )}{y ^{8}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d y} ( sec ( y ) ) y ^{8} - \frac{d}{d y} ( y ^{8} ) sec ( y )}{( y ^{8} ) ^{2}}

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

\frac{d}{d y} (y^{8}) = 8 y^{7}

= \frac{sec ( y ) tan ( y ) y ^{8} - 8 y ^{7} sec ( y )}{( y ^{8} ) ^{2}}

Simplify

\frac{sec ( y ) tan ( y ) y ^{8} - 8 y ^{7} sec ( y )}{( y ^{8} ) ^{2}} : \frac{sec ( y ) ( y tan ( y ) - 8 )}{y ^{9}}

= \frac{sec ( y ) ( y tan ( y ) - 8 )}{y ^{9}}

\int \frac{1}{e ^{x} ( e ^{x} + 1 )} d x

((x - 2)^{2})^{^{'}}

y^{^{'}} = \frac{2 x}{cos ( y )}

\int_{0}^{1.25} 1000 x d x

What is the derivative of (sec(y))/(y^8) ?
The derivative of (sec(y))/(y^8) is (sec(y)(ytan(y)-8))/(y^9)
What is the first derivative of (sec(y))/(y^8) ?
The first derivative of (sec(y))/(y^8) is (sec(y)(ytan(y)-8))/(y^9)