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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(2\ln\left(3x+22\right)+\ln\left(-9+e^{2x}\right)-\frac{3}{4}\ln\left(6x^2+2\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using logarithmic differentiation method ln(((3x+22)^2(-9+e^(2x)))/((6x^2+2)^3^1/4)). Simplify the derivative by applying the properties of logarithms. 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}.