What is (\partial)/(\partial x)(tan(6+2x^2y^4z^2)) ?

The answer to (\partial)/(\partial x)(tan(6+2x^2y^4z^2)) is sec^2(6+2x^2y^4z^2)*4y^4z^2x

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(\partial)/(\partial x)(tan(6+2x^2y^4z^2))

\frac{\partial}{\partial x} (tan (6 + 2 x^{2} y^{4} z^{2}))

sec^{2} (6 + 2 x^{2} y^{4} z^{2}) \cdot 4 y^{4} z^{2} x

Solution steps

\frac{\partial}{\partial x} (tan (6 + 2 x^{2} y^{4} z^{2}))

Treat

y, z

as constants

Apply the chain rule:

sec^{2} (6 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial x} (6 + 2 x^{2} y^{4} z^{2})

= sec^{2} (6 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial x} (6 + 2 x^{2} y^{4} z^{2})

\frac{\partial}{\partial x} (6 + 2 x^{2} y^{4} z^{2}) = 4 y^{4} z^{2} x

= sec^{2} (6 + 2 x^{2} y^{4} z^{2}) \cdot 4 y^{4} z^{2} x

\int 9 csc^{2} (x) d x

\int_{2}^{5} x d x

x \to 11 lim (x^{2})

\frac{d}{d t} (sec (t))

\int \frac{1}{( 2 y + 3 ) ^{2}} d y

What is (\partial)/(\partial x)(tan(6+2x^2y^4z^2)) ?
The answer to (\partial)/(\partial x)(tan(6+2x^2y^4z^2)) is sec^2(6+2x^2y^4z^2)*4y^4z^2x