What is (\partial)/(\partial y)(tan(3x-5y)) ?

The answer to (\partial)/(\partial y)(tan(3x-5y)) is -5sec^2(3x-5y)

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(\partial)/(\partial y)(tan(3x-5y))

\frac{\partial}{\partial y} (tan (3 x - 5 y))

- 5 sec^{2} (3 x - 5 y)

Solution steps

\frac{\partial}{\partial y} (tan (3 x - 5 y))

Treat

x

as a constant

Apply the chain rule:

sec^{2} (3 x - 5 y) \frac{\partial}{\partial y} (3 x - 5 y)

= sec^{2} (3 x - 5 y) \frac{\partial}{\partial y} (3 x - 5 y)

\frac{\partial}{\partial y} (3 x - 5 y) = - 5

= sec^{2} (3 x - 5 y) (- 5)

Simplify

= - 5 sec^{2} (3 x - 5 y)

2^{40}

\frac{\partial}{\partial x} (2 h (x) c^{2})

\int x e^{- 6 x} d x

\frac{d}{d x} (2 x^{2} cos (6 x))

\int csc (2 x) d x

What is (\partial)/(\partial y)(tan(3x-5y)) ?
The answer to (\partial)/(\partial y)(tan(3x-5y)) is -5sec^2(3x-5y)