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Find the derivative of $y=9 x^{2}+6^{x}+6$.
\[
\frac{d y}{d x}=
\]

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Answer

So, the derivative of the function $y=9x^2+6^x+6$ is $\boxed{18x+6^x \ln 6}$

Steps

Step 1 ：Rewrite the function as $y=9x^2+e^{x \ln 6}+6$

Step 2 ：Apply the power rule to find the derivative of $9x^2$, which is $18x$

Step 3 ：Apply the chain rule to find the derivative of $e^{x \ln 6}$, which is $e^{x \ln 6} \cdot \ln 6 = 6^x \ln 6$

Step 4 ：The derivative of a constant, like $6$, is $0$

Step 5 ：Combine the derivatives to get $\frac{d y}{d x}=18x+6^x \ln 6+0$

Step 6 ：Simplify to get $\frac{d y}{d x}=18x+6^x \ln 6$

Step 7 ：So, the derivative of the function $y=9x^2+6^x+6$ is $\boxed{18x+6^x \ln 6}$