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Popular >

derivative of (tan^2(x)/2)

Solution

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

Solution

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)

Popular Examples

derivative of e^{3x+3}

\frac{d}{d x} (e^{3 x + 3})

integral of 1/(2x^2-5x+7)

\int \frac{1}{2 x ^{2} - 5 x + 7} d x

integral of (x+1)e^{x^2+2x}

\int (x + 1) e^{x^{2} + 2 x} d x

derivative of g(t)=t^2-7/(t^3)derivative of

g (t) = t^{2} - \frac{7}{t ^{3}}

limit as x approaches 0 of ((343+x)^{1/3}-7)/x

x \to 0 lim (\frac{( 343 + x ) ^{\frac{1}{3}} - 7}{x})

Frequently Asked Questions (FAQ)

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)