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

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

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

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

sec^{2} (2 x + y)

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

0 = 2 x + 1 - 2 y y^{^{'}}

\int 2 [1 - cos^{2} (2 x)] d x

\int cos (x) (2 + sin (x))^{6} d x

\frac{d y}{d t} + t y^{2} = 0

\frac{4 x}{e ^{x}}

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