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Popular >

derivative of 1/2 sec^2(x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of x^{2/3}-a^{2/3}

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

integral from 0 to 1 of x^3sqrt(1-x^4)

\int_{0}^{1} x^{3} 1 - x^{4} d x

derivative of y(X)=(2X+5)/(sqrt(X))derivative of

y (X) = \frac{2 X + 5}{X}

(\partial)/(\partial x)(8ysqrt(x))

\frac{\partial}{\partial x} (8 y x)

limit as h approaches 0 of ((2+h)-2)/h

h \to 0 lim (\frac{( 2 + h ) - 2}{h})

Frequently Asked Questions (FAQ)

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