What is the derivative of-2/(cos(2x)+8/3) ?

The derivative of-2/(cos(2x)+8/3) is -4sec(2x)tan(2x)

What is the first derivative of-2/(cos(2x)+8/3) ?

The first derivative of-2/(cos(2x)+8/3) is -4sec(2x)tan(2x)

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\frac{d}{d x} (- \frac{2}{cos ( 2 x )} + \frac{8}{3})

- 4 sec (2 x) tan (2 x)

Solution steps

\frac{d}{d x} (- \frac{2}{cos ( 2 x )} + \frac{8}{3})

Simplify

- \frac{2}{cos ( 2 x )} + \frac{8}{3} : - 2 sec (2 x) + \frac{8}{3}

= \frac{d}{d x} (- 2 sec (2 x) + \frac{8}{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (2 sec (2 x)) + \frac{d}{d x} (\frac{8}{3})

\frac{d}{d x} (2 sec (2 x)) = 4 sec (2 x) tan (2 x)

\frac{d}{d x} (\frac{8}{3}) = 0

= - 4 sec (2 x) tan (2 x) + 0

Simplify

= - 4 sec (2 x) tan (2 x)

What is the derivative of-2/(cos(2x)+8/3) ?
The derivative of-2/(cos(2x)+8/3) is -4sec(2x)tan(2x)
What is the first derivative of-2/(cos(2x)+8/3) ?
The first derivative of-2/(cos(2x)+8/3) is -4sec(2x)tan(2x)