What is (\partial)/(\partial u)(tan(uv^3)) ?

The answer to (\partial)/(\partial u)(tan(uv^3)) is sec^2(uv^3)v^3

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(\partial)/(\partial u)(tan(uv^3))

\frac{\partial}{\partial u} (tan (u v^{3}))

sec^{2} (u v^{3}) v^{3}

Solution steps

\frac{\partial}{\partial u} (tan (u v^{3}))

Treat

v

as a constant

Apply the chain rule:

sec^{2} (u v^{3}) \frac{\partial}{\partial u} (u v^{3})

= sec^{2} (u v^{3}) \frac{\partial}{\partial u} (u v^{3})

\frac{\partial}{\partial u} (u v^{3}) = v^{3}

= sec^{2} (u v^{3}) v^{3}

(x y^{2} + x^{3}) d x + (y^{3} + x^{2} y) d y = 0

\frac{d}{d x} (tan (cos (x)))

\frac{d y}{d x}, y = x

\int \frac{1}{x ^{2} + 2 x} d x

\int (4 - 3 sin (2 x))^{4} cos (2 x) d x

What is (\partial)/(\partial u)(tan(uv^3)) ?
The answer to (\partial)/(\partial u)(tan(uv^3)) is sec^2(uv^3)v^3