Find the derivative of $\ln\left(\frac{\sqrt{-x+4}}{e^{\left(x^2\right)}\cos\left(3x^2+x\right)}\right)$

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

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(((-x+4)^(1/2))/(e^x^2cos(3x^2+x))). 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 power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.