Differentiate the following with respect of `x :log(1/(sqrt(x)))+5x^a-3a^x+root(3)(x^2)+6 root(4)(x^(-3))`

Explanation

To differentiate the function \( f(x) = \log\left(\frac{1}{\sqrt{x}}\right) + 5x^a - 3a^x + \sqrt[3]{x^2} + 6\sqrt[4]{x^{-3}} \), we will follow these steps:

### Step 1: Simplify the function
We can simplify \( f(x) \) using properties of logarithms and exponents:
\[ f(x) = \log(1) - \log(\sqrt{x}) + 5x^a - 3a^x + \sqrt[3]{x^2} + 6\sqrt[4]{x^{-3}} \]
Since \( \log(1) = 0 \), this simplifies to:
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