If 2/5x^3, find d/dx x=4

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tjillian87

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This is an extra credit calculus problem that has me stumped.

I thought that since y is f(x), I needed to find the derivative of y, and then plug in f prime, which is 4. The derivative of 2/5x^3 is -6/5^-4. If you plug in f prime 4 to the derivative, you get -24/625. I am so confused.
 
tjillian87 said:
This is an extra credit calculus problem that has me stumped.

I thought that since y is f(x), I needed to find the derivative of y, and then plug in f prime, which is 4. The derivative of 2/5x^3 is -6/5^-4. If you plug in f prime 4 to the derivative, you get -24/625. I am so confused.
Click to expand...

How did you get that?! It is incorrect.

It looks like you have:

y = 2/(5*x^3) = 2/5 * x^(-3)

and you need to calculate y' at x = 4

If y = a* x^n then y' = a * n * x^(n-1)

Now continue....
 
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Subhotosh Khan said:
How did you get that?! It is incorrect.

It looks like you have:

y = 2/(5*x^3) = 2/5 * x^(-3)

and you need to calculate y' at x = 4

If y = a* x^n then y' = a * n * x^(n-1)

Now continue....
Click to expand...

But the x here is not multiplication, but the variable x. 2/5 is a constant, while x^3 is found using the power rule of the function.
 
What also concerns me is the original function in the problem. What is the question trying to say? F prime has a value of 4, while the original function is not in its derived form.
 
Your initial thought was correct. You are being asked to find the derivative at the moment when x is 4. To do that, find the general form of the derivative and plug in x=4. Now, your reply where you say "No, it is y=2/5×^3..." seems to indicate that the function you need to find the derivative of is this:

\(\displaystyle \frac{2}{5}x^3\)

Is that correct? If so, apply the power rule. What do you get as the derivative? If that's not correct, then the function is probably this instead:

\(\displaystyle \frac{2}{5x^3}\)

If that's correct, then try rewriting the expression like this:

\(\displaystyle \frac{2}{5x^3}=\frac{2}{5}\cdot \frac{1}{x^3}\)

From there, can you see how to get it into the form that Khan gave you? After that, apply the power rule. What do you get as the derivative?

In either case, once you have your derivative, plug in x=4 and you have your answer.
 
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