Find the derivative of $f(x)=10 x$.

Step 1: Recall the Power Rule

To find the derivative of $f(x) = 10x$, we will use the power rule of differentiation. The power rule states that the derivative of $x$ raised to the power of $n$ is $n$ times $x$ raised to the power of $n-1$. In our case, $x$ is raised to the power of 1, so $n=1$.

Step 2: Apply the Constant Multiple Rule

The constant multiple rule states that if a function is multiplied by a constant, its derivative is the constant multiplied by the derivative of the function. Here, the constant is 10 and the function is $x$.

Step 3: Differentiate the function

Applying both the constant multiple rule and the power rule, we take the constant 10 outside and differentiate $x$. The derivative of $x^1$ is $1 \cdot x^{1-1}$, which simplifies to $1 \cdot x^0$.

Step 4: Simplify the expression

Since any non-zero number raised to the power of 0 is 1, $x^0$ becomes 1. Therefore, the derivative simplifies to $10 \cdot 1$, which is 10.

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