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.

3. Techniques of Differentiation

Basic Rules of Differentiation

Calculus

3. Techniques of Differentiation

Basic Rules of Differentiation

Calculus 때문에 힘들어하고 계신가요?

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객관식

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

$4x^3$

$24x^3$

$4x^3-1$

$24x^3-1$

검증된 단계별 안내

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.

4:09m

다음 시청

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전문가 영상 설명

Calculus 때문에 힘들어하고 계신가요?

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

다음 시청

Basic Rules of Differentiation 연습 세트

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