Find the derivative of f(x)=10x.
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Step-by-Step Solution
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 x1 is 1⋅x1−1, which simplifies to 1⋅x0.
Step 4: Simplify the expression
Since any non-zero number raised to the power of 0 is 1, x0 becomes 1. Therefore, the derivative simplifies to 10⋅1, which is 10.