140/MR00. problem / Math - Solved Math Problems

MR-140 / 140. problem

Find the first derivative of the function below:

$y = 9^{6 x + \sqrt{x}}$

$y = 9^{6 x + \sqrt{x}}$

$g (x) = 6 x + \sqrt{x}$

$g^{'} (x) = 6 + \frac{1}{2} \cdot x^{- \frac{1}{2}} = 6 + \frac{1}{2 \sqrt{x}}$

$y^{'} = 9^{g (x)} g' (x) \cdot \ln 9$

$y' = 9^{6 x + \sqrt{x}} \cdot (6 + \frac{1}{2 \sqrt{x}}) \cdot \ln 9$

$y^{'} = 9^{6 x + \sqrt{x}} \cdot (6 + \frac{1}{2 \sqrt{x}}) \cdot \ln 9$

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