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

The answer to (\partial)/(\partial x)(tan(3x^2+2x)) is sec^2(3x^2+2x)(6x+2)

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

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

sec^{2} (3 x^{2} + 2 x) (6 x + 2)

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (3 x^{2} + 2 x) = 6 x + 2

= sec^{2} (3 x^{2} + 2 x) (6 x + 2)

What is (\partial)/(\partial x)(tan(3x^2+2x)) ?
The answer to (\partial)/(\partial x)(tan(3x^2+2x)) is sec^2(3x^2+2x)(6x+2)