What is the derivative of sec^3(4x) ?

The derivative of sec^3(4x) is 12sec^3(4x)tan(4x)

What is the first derivative of sec^3(4x) ?

The first derivative of sec^3(4x) is 12sec^3(4x)tan(4x)

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\frac{d}{d x} (sec^{3} (4 x))

12 sec^{3} (4 x) tan (4 x)

Solution steps

\frac{d}{d x} (sec^{3} (4 x))

Apply the chain rule:

3 (sec (4 x))^{2} \frac{d}{d x} (sec (4 x))

= 3 (sec (4 x))^{2} \frac{d}{d x} (sec (4 x))

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

= 3 (sec (4 x))^{2} sec (4 x) tan (4 x) \cdot 4

Simplify

3 sec^{2} (4 x) sec (4 x) tan (4 x) \cdot 4 : 12 sec^{3} (4 x) tan (4 x)

= 12 sec^{3} (4 x) tan (4 x)

cos (t + \frac{π}{5})

\int cos (4 t) - sin (4 t) d t

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

\frac{d}{d x} (e^{9 x^{2}})

x^{^{''}} + 2 x = 0

What is the derivative of sec^3(4x) ?
The derivative of sec^3(4x) is 12sec^3(4x)tan(4x)
What is the first derivative of sec^3(4x) ?
The first derivative of sec^3(4x) is 12sec^3(4x)tan(4x)