What is (\partial)/(\partial y)(tan(3x-2y+1)) ?

The answer to (\partial)/(\partial y)(tan(3x-2y+1)) is -2sec^2(3x-2y+1)

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(\partial)/(\partial y)(tan(3x-2y+1))

\frac{\partial}{\partial y} (tan (3 x - 2 y + 1))

- 2 sec^{2} (3 x - 2 y + 1)

Solution steps

\frac{\partial}{\partial y} (tan (3 x - 2 y + 1))

Treat

x

as a constant

Apply the chain rule:

sec^{2} (3 x - 2 y + 1) \frac{\partial}{\partial y} (3 x - 2 y + 1)

= sec^{2} (3 x - 2 y + 1) \frac{\partial}{\partial y} (3 x - 2 y + 1)

\frac{\partial}{\partial y} (3 x - 2 y + 1) = - 2

= sec^{2} (3 x - 2 y + 1) (- 2)

Simplify

= - 2 sec^{2} (3 x - 2 y + 1)

What is (\partial)/(\partial y)(tan(3x-2y+1)) ?
The answer to (\partial)/(\partial y)(tan(3x-2y+1)) is -2sec^2(3x-2y+1)