What is (\partial)/(\partial y)(3tan(xy)) ?

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

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(\partial)/(\partial y)(3tan(xy))

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

3 sec^{2} (x y) x

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{\partial}{\partial y} (tan (x y))

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x y) = x

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

\frac{d y}{d x} = 3 (y^{2} + 1)

\frac{\partial}{\partial x} (2 x y e^{x y^{2}})

f (x) = tan (x), (\frac{π}{4}, 1)

\int \frac{4}{x ^{2} + 2 x + 5} d x

y (1 + x^{2}) y^{^{'}} - x (8 + y^{2}) = 0

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