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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{\arccos\left(\frac{1}{\sqrt{x}}\right)}\frac{d}{dx}\left(\arccos\left(\frac{1}{\sqrt{x}}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule d/dx(ln(arccos(1/(x^1/2)))). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Taking the derivative of arccosine. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Multiplying fractions \frac{1}{\arccos\left(\frac{1}{\sqrt{x}}\right)} \times \frac{-1}{\sqrt{1-\frac{1}{x}}}.