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Find the derivative of $\mathrm{arcsec}\left(\sqrt{x}\right)$

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Solution

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Final answer to the problem

$\frac{1}{2x\sqrt{x-1}}$
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Step-by-step Solution

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Learn how to solve power rule for derivatives problems step by step online. Find the derivative of arcsec(x^(1/2)). Taking the derivative of arcsecant. Cancel exponents \frac{1}{2} and 2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiplying fractions \frac{1}{\sqrt{x}\sqrt{x-1}} \times \frac{1}{2}.

Final answer to the problem

$\frac{1}{2x\sqrt{x-1}}$

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Function Plot

Plotting: $\frac{1}{2x\sqrt{x-1}}$

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◻/◻
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◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

$\frac{d}{dx}\left(\arcsin\left(x^3\right)\right)$

$\frac{d}{dx}\arcsin\left(\sqrt{x}\right)$

$\frac{d}{dx}\left(\arcsin\left(\sqrt{2x}\right)\right)$

$\frac{d}{dx}\left(\arccot\left(\sqrt{x}\right)\right)$

$\frac{d}{dx}\left(\arcsin\sqrt{x}\right)$

$\frac{d}{dx}\left(\arctan\left(x-\sqrt{1+x^2}\right)\right)$

$\frac{d}{dx}\arccos\left(\sqrt{x}\right)$

Main Topic: Power Rule for Derivatives

The power rule is used to differentiate functions of the form f(x)=x^a, when a is a real number.

Used Formulas

See formulas (2)

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