What is (\partial)/(\partial x)(sec^2(xy)) ?

The answer to (\partial)/(\partial x)(sec^2(xy)) is 2ysec^2(xy)tan(xy)

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(\partial)/(\partial x)(sec^2(xy))

\frac{\partial}{\partial x} (sec^{2} (x y))

2 y sec^{2} (x y) tan (x y)

Solution steps

\frac{\partial}{\partial x} (sec^{2} (x y))

Treat

y

as a constant

Apply the chain rule:

2 sec (x y) \frac{\partial}{\partial x} (sec (x y))

= 2 sec (x y) \frac{\partial}{\partial x} (sec (x y))

\frac{\partial}{\partial x} (sec (x y)) = sec (x y) tan (x y) y

= 2 sec (x y) sec (x y) tan (x y) y

Simplify

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

= 2 y sec^{2} (x y) tan (x y)

n = 1 \sum \infty \frac{3}{π ^{n}}

x^{\frac{1}{3}} - x^{- \frac{2}{3}}

x \to + 0 lim (2 x^{2} cos (\frac{5}{x}))

\frac{\partial}{\partial x} (e^{x} - 2 - cos (x y))

\frac{d}{d x} (\frac{3}{5 + x})

What is (\partial)/(\partial x)(sec^2(xy)) ?
The answer to (\partial)/(\partial x)(sec^2(xy)) is 2ysec^2(xy)tan(xy)