What is (\partial)/(\partial x)(sec(xy)+tan(xy)) ?

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

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(\partial)/(\partial x)(sec(xy)+tan(xy))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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