What is the derivative of 1/3 sec^3(2x-sec(2x)) ?

The derivative of 1/3 sec^3(2x-sec(2x)) is 2tan^3(2x)sec(2x)

What is the first derivative of 1/3 sec^3(2x-sec(2x)) ?

The first derivative of 1/3 sec^3(2x-sec(2x)) is 2tan^3(2x)sec(2x)

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\frac{d}{d x} (\frac{1}{3} sec^{3} (2 x) - sec (2 x))

2 tan^{3} (2 x) sec (2 x)

Solution steps

\frac{d}{d x} (\frac{1}{3} sec^{3} (2 x) - sec (2 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{3} sec^{3} (2 x)) - \frac{d}{d x} (sec (2 x))

\frac{d}{d x} (\frac{1}{3} sec^{3} (2 x)) = 2 sec^{3} (2 x) tan (2 x)

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

= 2 sec^{3} (2 x) tan (2 x) - sec (2 x) tan (2 x) \cdot 2

Simplify

2 sec^{3} (2 x) tan (2 x) - sec (2 x) tan (2 x) \cdot 2 : 2 tan^{3} (2 x) sec (2 x)

= 2 tan^{3} (2 x) sec (2 x)

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

x \to 1 lim (\frac{x ^{3}}{x ^{2} - 1})

f (x) = 6^{7 x^{2}}

\int - \frac{1}{x + 1} d x

\frac{\partial}{\partial x} (x^{2} y - 3 y^{4})

What is the derivative of 1/3 sec^3(2x-sec(2x)) ?
The derivative of 1/3 sec^3(2x-sec(2x)) is 2tan^3(2x)sec(2x)
What is the first derivative of 1/3 sec^3(2x-sec(2x)) ?
The first derivative of 1/3 sec^3(2x-sec(2x)) is 2tan^3(2x)sec(2x)