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

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

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(\partial)/(\partial x)(tan(xy^3))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

9 y^{^{''}} + 6 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 2

(7 x^{2} - 11 x) e^{x}

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

\frac{d}{d x} (x^{5} - e^{x} ln (x))

x \to - \infty lim (5 x)

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