What is the derivative of sec(2xtan(2x)) ?

The derivative of sec(2xtan(2x)) is 2tan^2(2x)sec(2x)+2sec^3(2x)

What is the first derivative of sec(2xtan(2x)) ?

The first derivative of sec(2xtan(2x)) is 2tan^2(2x)sec(2x)+2sec^3(2x)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (2 x), g = tan (2 x)

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x - z - arctan (yz))

f (x) = \frac{x ^{3}}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} (\frac{cos ( x )}{x})

\frac{d}{d x} (- \frac{3}{4} x^{\frac{1}{3}})

y^{^{'}} - \frac{3 y}{x} = x

What is the derivative of sec(2xtan(2x)) ?
The derivative of sec(2xtan(2x)) is 2tan^2(2x)sec(2x)+2sec^3(2x)
What is the first derivative of sec(2xtan(2x)) ?
The first derivative of sec(2xtan(2x)) is 2tan^2(2x)sec(2x)+2sec^3(2x)