Find the indicated derivative. f ( x ) = 6 x 4 − 4 3 f(x)=6x^4-4^3 f ( x ) = 6 x 4 − 4 3 f ′ ( x ) = f^{\prime}\left(x\right)= f ′ ( x ) =

In this problem, we're asked to find the derivative f prime of x of our function f of x, which is 6x to the power of 4 minus 4 cubed. So let's go ahead and get started here. Now, again, I'm going to fully break this one down using all of the rules that we know. So let's go ahead and jump right in. Now here for my first term, I had that 6x to the power of 4. Now in thinking about this derivative, since I have a constant here, I know that I can really just pull that constant out of the derivative. So this derivative is 6 times derivative d d x of x to the power of 4, effectively just pulling that 6 out to the front. Then I'm subtracting the derivative d d x of 4 cubed. Now let's go ahead and actually take these derivatives. So 6 times the d d x of x to the power of 4. In order to take this derivative here, I know that I need to use the power rule. Now my constant here, 6, is going to stay as is. And when using the power rule, I'm gonna pull that 4 out to the front and then decrease that exponent by 1. So the derivative of x to the power of 4 is going to be 4x cubed. Having decreased that exponent by 1, 4 minus 1 gives me my new power of 3. Now here, I'm going to subtract the derivative of 4 cubed. Now a common mistake here, because this is 4 to the power of something, is to want to use the power rule. But let's think about what 4 cubed is. 4 cubed is just 4 times 4 times 4. That's just a constant. So we don't need to use the power rule here because there is no variable. This is just a constant, and the derivative of any constant is just 0. So here, we're effectively subtracting 0, which is doing nothing to our function. So we can further simplify this. 6 times 4 is 24. This is 24 x cubed for the derivative f prime of x. And we are all done here. Let me know if you have any questions and let's continue practicing.

Find the indicated derivative. f ( x ) = 6 x 4 − 4 3 f(x)=6x^4-4^3 f ( x ) = 6 x 4 − 4 3 f ′ ( x ) = f^{\prime}\left(x\right)= f ′ ( x ) =

24 x 3 − 1 24x^3-1 24 x 3 − 1

3. Techniques of Differentiation

Basic Rules of Differentiation

Calculus

3. Techniques of Differentiation

Basic Rules of Differentiation

Struggling with Calculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Find the indicated derivative.
$f(x)=6x^4-4^3$
$f^{\prime}\left(x\right)=$

$4x^3$

$24x^3$

$4x^3-1$

$24x^3-1$

Verified step by step guidance

First, identify the function you need to differentiate: f(x) = 6x^4 - 4^3.

Recognize that the function is a polynomial, and apply the power rule for differentiation. The power rule states that if f(x) = ax^n, then f'(x) = n * ax^(n-1).

Apply the power rule to the term 6x^4. Differentiate it to get: f'(x) = 4 * 6x^(4-1).

The term -4^3 is a constant, and the derivative of a constant is zero. Therefore, it does not contribute to the derivative.

Combine the results from the differentiation: f'(x) = 24x^3.

3:59m

Watch next

Master Derivatives of Linear Functions with a bite sized video explanation from Patrick

Start learning

Basic Rules of Differentiation practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice

Struggling with Calculus?

Find the indicated derivative.f(x)=6x4−43f(x)=6x^4-4^3f(x)=6x4−43f′(x)=f^{\prime}\left(x\right)=f′(x)=

Watch next

Basic Rules of Differentiation practice set

Find the indicated derivative.
$f(x)=6x^4-4^3$
$f^{\prime}\left(x\right)=$