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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

y = \frac{x ^{7}}{f ( x )}

\frac{d}{d x} (x^{7} e^{9 x})

f (x) = \frac{16 x}{x ^{2} + 16}

h \to 0 lim (\frac{( π + h ) + 1}{h})

\frac{d}{d x} (\frac{( x ^{2} - 3 x )}{4 x + 1})

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