Problem 9
Question
Find the derivative of the function. $$ f(x)=4 x+1 $$
Step-by-Step Solution
Verified Answer
The derivative of the function \(f(x) = 4x + 1\) is \(4\).
1Step 1: Identify the terms of the function
The function \(f(x) = 4x + 1\) is composed of two terms, namely \(4x\) and \(1\).
2Step 2: Calculate the derivative of each term
Following the power rule, the derivative of \(4x\) is \(4*1*x^{1-1} = 4\) and the derivative of a constant function like \(1\) is \(0\).
3Step 3: Sum up the derivatives of each term
The derivative of the function \(f(x)\) or \(f'(x)\) is then the sum of the individual derivatives, which is \(4 + 0 = 4\).
Other exercises in this chapter
Problem 9
Find the value of the derivative of the function at the given point. State which differentiation rule you used to find the derivative. $$ h(x)=\frac{x}{x-5} $$
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Determine whether the function is continuous on the entire real line. Explain your reasoning. \(g(x)=\frac{x^{2}-4 x+4}{x^{2}-4}\)
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Find \(d y / d u, d u / d x\), and \(d y / d x\). $$ y=u^{3}, u=3 x^{2}-2 $$
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