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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\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}

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