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Popular >

derivative of sec^2(pix)

Solution

derivative of

sec^{2} (π x)

Solution

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)

Popular Examples

derivative of 6/(x+2)

\frac{d}{d x} (\frac{6}{x + 2})

tangent of f(x)=(2+3x)(6-5x),\at x=1 tangent of

f (x) = (2 + 3 x) (6 - 5 x), at x = 1

derivative of e^{(3-x})

\frac{d}{d x} (e^{(3 - x)})

derivative of xe^{-3x}

\frac{d}{d x} (x e^{- 3 x})

integral of cos(x)(4+4sin^2(x))

\int cos (x) (4 + 4 sin^{2} (x)) d x

Frequently Asked Questions (FAQ)

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)