What is the derivative of (8-sec(x))/(tan(x)) ?

The derivative of (8-sec(x))/(tan(x)) is (-tan^2(x)sec(x)-sec^2(x)(8-sec(x)))/(tan^2(x))

What is the first derivative of (8-sec(x))/(tan(x)) ?

The first derivative of (8-sec(x))/(tan(x)) is (-tan^2(x)sec(x)-sec^2(x)(8-sec(x)))/(tan^2(x))

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derivative of

\frac{8 - sec ( x )}{tan ( x )}

\frac{- tan ^{2} ( x ) sec ( x ) - sec ^{2} ( x ) ( 8 - sec ( x ) )}{tan ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{8 - sec ( x )}{tan ( x )})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (8 - sec (x)) = - sec (x) tan (x)

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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

Simplify

\frac{( - sec ( x ) tan ( x ) ) tan ( x ) - sec ^{2} ( x ) ( 8 - sec ( x ) )}{tan ^{2} ( x )} : \frac{- tan ^{2} ( x ) sec ( x ) - sec ^{2} ( x ) ( 8 - sec ( x ) )}{tan ^{2} ( x )}

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

\int \frac{e ^{- y}}{y} d y

\int_{0}^{2} (x - 1)^{2} d x

\frac{\partial}{\partial x} (5 - x^{2} + x y - 2^{2})

\frac{d}{d x} ((x^{3} + 4)^{- 3})

What is the derivative of (8-sec(x))/(tan(x)) ?
The derivative of (8-sec(x))/(tan(x)) is (-tan^2(x)sec(x)-sec^2(x)(8-sec(x)))/(tan^2(x))
What is the first derivative of (8-sec(x))/(tan(x)) ?
The first derivative of (8-sec(x))/(tan(x)) is (-tan^2(x)sec(x)-sec^2(x)(8-sec(x)))/(tan^2(x))