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

The derivative of xsec^2(pix) is sec^2(pix)+2pixsec^2(pix)tan(pix)

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

The first derivative of xsec^2(pix) is sec^2(pix)+2pixsec^2(pix)tan(pix)

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\frac{d}{d x} (x sec^{2} (π x))

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

Solution steps

\frac{d}{d x} (x sec^{2} (π x))

Apply the Product Rule:

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

f = x, g = sec^{2} (π x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot sec^{2} (π x) + 2 π sec^{2} (π x) tan (π x) x

Simplify

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

x \to - 0 lim (2 x e^{2 x} + k x)

\int 1 + \frac{2}{t} d t

\int cot (17 x) d x

\int (cos (x) + \frac{1}{3} x) d x

\int e^{x - 1} + x^{- 2} d x

What is the derivative of xsec^2(pix) ?
The derivative of xsec^2(pix) is sec^2(pix)+2pixsec^2(pix)tan(pix)
What is the first derivative of xsec^2(pix) ?
The first derivative of xsec^2(pix) is sec^2(pix)+2pixsec^2(pix)tan(pix)