What is the derivative of sec^2(pix) ?

The derivative of sec^2(pix) is 2pisec^2(pix)tan(pix)

What is the first derivative of sec^2(pix) ?

The first derivative of sec^2(pix) is 2pisec^2(pix)tan(pix)

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\frac{d}{d x} (sec^{2} (π x))

2 π sec^{2} (π x) tan (π x)

Solution steps

\frac{d}{d x} (sec^{2} (π x))

Apply the chain rule:

2 sec (π x) \frac{d}{d x} (sec (π x))

= 2 sec (π x) \frac{d}{d x} (sec (π x))

\frac{d}{d x} (sec (π x)) = sec (π x) tan (π x) π

= 2 sec (π x) sec (π x) tan (π x) π

Simplify

2 sec (π x) sec (π x) tan (π x) π : 2 π sec^{2} (π x) tan (π x)

= 2 π sec^{2} (π x) tan (π x)

What is the derivative of sec^2(pix) ?
The derivative of sec^2(pix) is 2pisec^2(pix)tan(pix)
What is the first derivative of sec^2(pix) ?
The first derivative of sec^2(pix) is 2pisec^2(pix)tan(pix)