What is (\partial)/(\partial y)(tan(x^3y^2)) ?

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

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(\partial)/(\partial y)(tan(x^3y^2))

\frac{\partial}{\partial y} (tan (x^{3} y^{2}))

sec^{2} (x^{3} y^{2}) \cdot 2 x^{3} y

Solution steps

\frac{\partial}{\partial y} (tan (x^{3} y^{2}))

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

\frac{\partial}{\partial x} (cos (x^{2} - y))

\int \frac{2 x}{x - 1} d x

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

4 y^{^{''}} - 4 y^{^{'}} + 4 y = 0

\frac{\partial}{\partial x} (x y + x cos (x))

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