What is the derivative of 1/3 tan^3(x/2-tan(x/2)) ?

The derivative of 1/3 tan^3(x/2-tan(x/2)) is 1/2 tan^2(x/2)sec^2(x/2)-sec^2(x/2) 1/2

What is the first derivative of 1/3 tan^3(x/2-tan(x/2)) ?

The first derivative of 1/3 tan^3(x/2-tan(x/2)) is 1/2 tan^2(x/2)sec^2(x/2)-sec^2(x/2) 1/2

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\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

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

Solution steps

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2}) - tan (\frac{x}{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2})) - \frac{d}{d x} (tan (\frac{x}{2}))

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{x}{2})) = \frac{1}{2} tan^{2} (\frac{x}{2}) sec^{2} (\frac{x}{2})

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

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

\frac{d}{d x} (sec^{4} (2) x^{2})

\frac{d}{d x} (n x^{n})

\frac{2 x ^{2} + 8 x + 4}{x}

\frac{d}{d x} (\frac{- cos ( x ) - 1}{x ^{3} + x ^{2}})

y = 1 + 4 x^{2} - 2 x^{3}

What is the derivative of 1/3 tan^3(x/2-tan(x/2)) ?
The derivative of 1/3 tan^3(x/2-tan(x/2)) is 1/2 tan^2(x/2)sec^2(x/2)-sec^2(x/2) 1/2
What is the first derivative of 1/3 tan^3(x/2-tan(x/2)) ?
The first derivative of 1/3 tan^3(x/2-tan(x/2)) is 1/2 tan^2(x/2)sec^2(x/2)-sec^2(x/2) 1/2