Find the derivative $\frac{d}{dx}\left(2\ln\left(\frac{4}{x}\right)+e^{3x^2}+4\left(\frac{x^2-1}{x^2+2}\right)\right)$ using the sum rule

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$\frac{d}{dx}\left(2\ln\left(4\right)-2\ln\left(x\right)+e^{3x^2}+4\left(\frac{x^2-1}{x^2+2}\right)\right)$

Learn how to solve integrals of rational functions problems step by step online. Find the derivative d/dx(2ln(4/x)+e^(3x^2)4(x^2-1)/(x^2+2)) using the sum rule. 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}.