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

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

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

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

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

sec^{2} (x) tan (x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= sec^{2} (x) tan (x)

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