Q. \[ \frac{d}{dx}\left(x^{4}\right) \]

We want to find the derivative of the function

\[
f(x)=x^{4}.
\]

Step 1: Identify the rule to use.

Because \(x^{4}\) is a power of \(x\), we use the power rule:

\[
\frac{d}{dx}\left(x^{n}\right)=n x^{n-1}.
\]

Step 2: Match the given function to the power rule.

Here, \(n=4\) because the exponent on \(x\) is \(4\).

Step 3: Apply the power rule.

Substitute \(n=4\) into the rule:

\[
\frac{d}{dx}\left(x^{4}\right)=4x^{4-1}.
\]

Step 4: Simplify the exponent.

\(4-1=3\), so:

\[
\frac{d}{dx}\left(x^{4}\right)=4x^{3}.
\]

Final Answer.

\[
\boxed{\frac{d}{dx}\left(x^{4}\right)=4x^{3}}
\]