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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - sec^{2} (\frac{x}{2}) tan (\frac{x}{2})

Simplify

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

\frac{1}{cos ( 2 x )}

5 \cdot sin^{2} (x) - 8 \cdot cos^{5} (x)

\frac{d}{d x} (x^{5} \cdot a + x^{5} \cdot b - a - b)

(x^{2} + 5 x) 5

2 - ∣ 3 - x ∣

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