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Chapter 7: Problem 10

Find the derivative of the function. $$ g(x)=3 x-1 $$

Short Answer

Expert verified
The derivative of \(g(x) = 3x - 1\) is 3.

Step by step solution

01

Identify the function

The function given in the problem is \(g(x) = 3x-1\).
02

Differentiate

Differentiate the function with respect to x. According to the power rule, the derivative of \(x^n\) is \(nx^{n-1}\). So, the derivative of \(x\) is 1. Multiply this by the coefficient of x in your function. Hence, the derivative of the function \(g(x)\) i.e. \(g'(x)\), is equal to \(3*1\), which equals 3.
03

Result

Thus, the derivative of the function \(g(x) = 3x - 1\) is 3.

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Most popular questions from this chapter

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ y=\left(\frac{6-5 x}{x^{2}-1}\right)^{2} $$

Use the General Power Rule to find the derivative of the function. $$ y=\sqrt[3]{3 x^{3}+4 x} $$

Use the given information to find \(f^{\prime}(2)\) \(g(2)=3\) and \(g^{\prime}(2)=-2\) \(h(2)=-1 \quad\) and \(\quad h^{\prime}(2)=4\) $$ f(x)=g(x)+h(x) $$

Use the General Power Rule to find the derivative of the function. $$ y=2 \sqrt{4-x^{2}} $$

The monthly sales of memberships \(M\) at a newly built fitness center are modeled by \(M(t)=\frac{300 t}{t^{2}+1}+8\) where \(t\) is the number of months since the center opened. (a) Find \(M^{\prime}(t)\). (b) Find \(M(3)\) and \(M^{\prime}(3)\) and interpret the results. (c) Find \(M(24)\) and \(M^{\prime}(24)\) and interpret the results.
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