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

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

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