Find the indicated derivative. f ( x ) = 3 x − 4 f(x)=3x-4 f ( x ) = 3 x − 4 f ′ ( x ) = f^{\prime}(x)= f ′ ( x ) =

Hey, everyone. In this problem, we're asked to find the derivative of the function f of x equals 3x minus 4. I'm going to fully break this down based on all of the rules for derivatives that we've learned. So let's go ahead and jump in. Now in finding the derivative, I'm going to denote that f prime of x. And in order to find the derivative here, since I have this constant 3 multiplying my x, I can pull that constant out to the front, and I'm really just taking that constant 3 and multiplying it by the derivative ddx of x. Then since I have some subtraction here, I am then subtracting the derivative ddx of that constant here, 4. Now from here, I can actually take these derivatives. I have this 3 multiplying the derivative of x, which we know is just 1. So this is 3 times 1. And then we're subtracting the derivative of 4, which is a constant, and the derivative of any constant is just 0. So this is 3 times 1 minus 0 or just 3. So my final answer here for the derivative of my function, 3x minus 4, is just 3. Now starting out here, I am going to break down these derivatives fully based on the rules that we've learned. But as we continue to take more and more derivatives, you're going to be able to just recognize just by looking at this original function that your derivative is 3. So I'm going to start breaking it down less as we get more and more familiar with these rules. Let me know if you have any questions here. Thanks for watching.

3. Techniques of Differentiation

Basic Rules of Differentiation

Calculus

3. Techniques of Differentiation

Basic Rules of Differentiation

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Multiple Choice

Find the indicated derivative.
$f(x)=3x-4$
$f^{\prime}(x)=$

$0$

$1$

$2$

$3$

Verified step by step guidance

Identify the function given: $ f(x) = 3x - 4 $. This is a linear function.

Recall that the derivative of a linear function $ f(x) = ax + b $ is simply the coefficient $ a $.

In this case, the coefficient $ a $ is 3, as seen in the term $ 3x $.

Therefore, the derivative $ f'(x) $ is the constant value of the coefficient of $ x $, which is 3.

Conclude that $ f'(x) = 3 $, as the derivative of a constant term $-4$ is zero.

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[Technology Exercise] c. Confirm your estimates of the coordinates of the second intersection point by solving the equations for the curve and tangent line simultaneously.

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Multiple Choice

Find the indicated derivative.

$d/dt(-5t)$