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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$-\ln\left(\sqrt{\arctan\left(x\right)}\right)^{-2}\frac{d}{dx}\left(\ln\left(\sqrt{\arctan\left(x\right)}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule y=ln(arctan(x)^1/2)^(-1). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. 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}. Multiplying the fraction by -1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.