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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{dx}\left(\ln\left(e^{4x}-1\right)\right)+\frac{d}{dx}\left(-\ln\left(e^{4x}+1\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(ln(e^(4x)-1)-ln(e^(4x)+1)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. 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.