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

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$\frac{d}{dx}\left(\sin\left(x^x\right)\right)+\frac{d}{dx}\left(x^{\sin\left(x\right)}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative d/dx(sin(x^x)+x^sin(x)) 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 the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative \frac{d}{dx}\left(x^x\right) results in \left(\ln\left(x\right)+1\right)x^x. The derivative \frac{d}{dx}\left(x^{\sin\left(x\right)}\right) results in \left(\cos\left(x\right)\ln\left(x\right)+\frac{\sin\left(x\right)}{x}\right)x^{\sin\left(x\right)}.