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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\ln\left(\arctan\left(\frac{x}{3}\right)\right)\right)$
Learn how to solve problems step by step online. Find the derivative of ln(arctan((x1)/3)). Simplify the derivative by applying the properties of logarithms. 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 arctangent. 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}.