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Popular >

derivative of y=sec^2(sqrt(x))

Solution

derivative of

y = sec^{2} (x)

Solution

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

Solution steps

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

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

Simplify

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

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

Popular Examples

limit as n approaches infinity of \sum_{i=1}^nsqrt((2i)/n)*2/n

n \to \infty lim (i = 1 \sum n \frac{2 i}{n} \cdot \frac{2}{n})

(\partial)/(\partial x)(1/(sqrt(x+2)))

\frac{\partial}{\partial x} (\frac{1}{x + 2})

tangent of f(x)=3x-4x^2,(-1,-7)tangent of

f (x) = 3 x - 4 x^{2}, (- 1, - 7)

integral of 5xsqrt(x+4)

\int 5 x x + 4 d x

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

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

Frequently Asked Questions (FAQ)

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