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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\int 5 arcsin (x) d x

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = 0

x \to 0 lim (\frac{8 ^{x} - 1}{x})

\frac{\partial}{\partial y} (\frac{x ^{4}}{6 y} + \frac{12 y ^{4}}{x})

\int 2 sin^{2} (θ) d θ

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