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

Business Calculus

3. Techniques of Differentiation

Basic Rules of Differentiation

Struggling with Business Calculus?

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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 given function: $ f(x) = 3x - 4 $. This is a linear function, where the derivative of a linear function is constant.

Recall the power rule for derivatives: $ \frac{d}{dx}[x^n] = n \cdot x^{n-1} $. For a term like $ 3x $, the exponent $ n $ is 1.

Apply the power rule to the term $ 3x $: The derivative of $ 3x $ is $ 3 \cdot 1 \cdot x^{1-1} = 3 \cdot x^0 = 3 $, since $ x^0 = 1 $.

Next, find the derivative of the constant term $ -4 $: The derivative of any constant is $ 0 $.

Combine the results: The derivative of $ f(x) = 3x - 4 $ is $ f'(x) = 3 + 0 = 3 $.

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Struggling with Business Calculus?

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

Watch next

Basic Rules of Differentiation practice set

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