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Chapter 7: Problem 9

Find the derivative of the function. $$ f(x)=4 x+1 $$

Short Answer

Expert verified
The derivative of the function \(f(x) = 4x + 1\) is \(4\).

Step by step solution

01

Identify the terms of the function

The function \(f(x) = 4x + 1\) is composed of two terms, namely \(4x\) and \(1\).
02

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 \(0\).
03

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 \(4 + 0 = 4\).

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Most popular questions from this chapter

Use the General Power Rule to find the derivative of the function. $$ s(t)=\sqrt{2 t^{2}+5 t+2} $$

Use the General Power Rule to find the derivative of the function. $$ h(t)=\left(1-t^{2}\right)^{4} $$

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Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=(6 x-5)^{4} $$
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