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Popular >

derivative of 1/2 tan^2(x)

Solution

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

Solution

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

Solution steps

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

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)

Graph

Popular Examples

integral of sqrt(e^x-3)

\int e^{x} - 3 d x

integral from-1 to 5 of (8x)/(x^2-4x-12)

\int_{- 1}^{5} \frac{8 x}{x ^{2} - 4 x - 12} d x

(\partial)/(\partial z)(x/y-y/z)

\frac{\partial}{\partial z} (\frac{x}{y} - \frac{y}{z})

integral of 1/((x-4)^{3/2)}

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

limit as x approaches 0 of x^{-5/(ln(x))}

x \to 0 lim (x^{- \frac{5}{l n ( x )}})

Frequently Asked Questions (FAQ)

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