What is (\partial)/(\partial x)(tan(x/2)) ?

The answer to (\partial)/(\partial x)(tan(x/2)) is sec^2(x/2) 1/2

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(\partial)/(\partial x)(tan(x/2))

\frac{\partial}{\partial x} (tan (\frac{x}{2}))

sec^{2} (\frac{x}{2}) \frac{1}{2}

Solution steps

\frac{\partial}{\partial x} (tan (\frac{x}{2}))

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x}{2}) = \frac{1}{2}

= sec^{2} (\frac{x}{2}) \frac{1}{2}

y^{^{'''}} + 4 y^{^{''}} - 35 y^{^{'}} - 150 y = 0

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

\frac{d}{d x} (cos^{2} (x^{2}))

\frac{d}{d x} (\frac{9 ^{x} - 1 5 ^{- x}}{x})

(6.3) (4.2)

What is (\partial)/(\partial x)(tan(x/2)) ?
The answer to (\partial)/(\partial x)(tan(x/2)) is sec^2(x/2) 1/2