What is (\partial)/(\partial x)(cos^2(x)+sin^2(y)) ?

The answer to (\partial)/(\partial x)(cos^2(x)+sin^2(y)) is -sin(2x)

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(\partial)/(\partial x)(cos^2(x)+sin^2(y))

\frac{\partial}{\partial x} (cos^{2} (x) + sin^{2} (y))

- sin (2 x)

Solution steps

\frac{\partial}{\partial x} (cos^{2} (x) + sin^{2} (y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (cos^{2} (x)) + \frac{\partial}{\partial x} (sin^{2} (y))

\frac{\partial}{\partial x} (cos^{2} (x)) = - sin (2 x)

\frac{\partial}{\partial x} (sin^{2} (y)) = 0

= - sin (2 x) + 0

Simplify

= - sin (2 x)

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\int \frac{6}{x ( x ^{2} + 4 ) ^{2}} d x

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What is (\partial)/(\partial x)(cos^2(x)+sin^2(y)) ?
The answer to (\partial)/(\partial x)(cos^2(x)+sin^2(y)) is -sin(2x)