Find the derivative of the function. \[ h(x)=\log _{3}\left(x^{2}+x\right) \] \[ h^{\prime}(x)= \] Submit Answer

Step 1 ：Given the function \(h(x)=\log _{3}\left(x^{2}+x\right)\)

Step 2 ：We need to find its derivative \(h^{\prime}(x)\)

Step 3 ：We use the chain rule, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function

Step 4 ：In this case, the outer function is the logarithm and the inner function is \(x^{2}+x\)

Step 5 ：The derivative of the logarithm base 3 of x is \(\frac{1}{x*\ln(3)}\)

Step 6 ：The derivative of \(x^{2}+x\) is \(2x+1\)

Step 7 ：So, the derivative of the function \(h(x)=\log _{3}\left(x^{2}+x\right)\) is \(\frac{1}{(x^{2}+x)*\ln(3)}*(2x+1)\)

Step 8 ：Finally, we simplify the derivative to get the final answer

Step 9 ：\(\boxed{h^{\prime}(x)=\frac{2x+1}{(x^{2}+x)\ln(3)}}\)