What is (\partial)/(\partial x)(tan(8+2x^2y^4z^2)) ?

The answer to (\partial)/(\partial x)(tan(8+2x^2y^4z^2)) is sec^2(8+2x^2y^4z^2)*4y^4z^2x

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(\partial)/(\partial x)(tan(8+2x^2y^4z^2))

\frac{\partial}{\partial x} (tan (8 + 2 x^{2} y^{4} z^{2}))

sec^{2} (8 + 2 x^{2} y^{4} z^{2}) \cdot 4 y^{4} z^{2} x

Solution steps

\frac{\partial}{\partial x} (tan (8 + 2 x^{2} y^{4} z^{2}))

Treat

y, z

as constants

Apply the chain rule:

sec^{2} (8 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial x} (8 + 2 x^{2} y^{4} z^{2})

= sec^{2} (8 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial x} (8 + 2 x^{2} y^{4} z^{2})

\frac{\partial}{\partial x} (8 + 2 x^{2} y^{4} z^{2}) = 4 y^{4} z^{2} x

= sec^{2} (8 + 2 x^{2} y^{4} z^{2}) \cdot 4 y^{4} z^{2} x

\frac{\partial}{\partial x} (324 x^{2} - 324 x y + 81 y^{2})

4 cos (3 x), 4 sin (6 x), 0, \frac{π}{6}

8 arcsin (x^{4})

\int_{0.1}^{0.2} 300 x d x

\int cos (x) d x

What is (\partial)/(\partial x)(tan(8+2x^2y^4z^2)) ?
The answer to (\partial)/(\partial x)(tan(8+2x^2y^4z^2)) is sec^2(8+2x^2y^4z^2)*4y^4z^2x