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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x^{2} + y) = 1

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

Simplify

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

arcsin (x^{5})

\frac{37500}{1 + 19 e ^{- 0.6 x}}

x \to 0 + lim (e^{x l n (x)})

\int (x^{2} + \frac{1}{x})^{2} d x

- 384 e^{- 4 x}

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