How do you find the derivative of $f (x) = \frac{6 tan x - 10}{sec x}$ $f(x)=( 6tanx-10)/secx$ ?

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Answer 1 · 2017-04-02T14:29:46

$f'(x)=6cosx+10sinx$

We can make this simpler by first simplifying the function:

$f(x)=(6tanx-10)/secx=(6(sinx/cosx)-10)/(1/cosx)$

$f(x)=cosx(6sinx/cosx-10)=6sinx-10cosx$

Now, all we need to know is that $d/dxsinx=cosx$ and $d/dxcosx=-sinx$ . Then:

$f'(x)=6cosx-10(-sinx)=6cosx+10sinx$

How do you find the derivative of f(x)=( 6tanx-10)/secxf(x)=6tanx−10secxf(x)=( 6tanx-10)/secx?