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

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

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(\partial)/(\partial x)(tan(x^2+y^2))

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

sec^{2} (x^{2} + y^{2}) \cdot 2 x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= sec^{2} (x^{2} + y^{2}) \cdot 2 x

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