Need homework help please : (

steffyfee

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Feb 22, 2010
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I'm doing a problem set for my calculus class and although I know this is a simple problem I forgot how to approach powers. It goes like this:

If y= (3x^4+5)^3, then dy/dx=

A) 3 (12x^3)^2

B) 36(3x^4 +5)^2

C) 36x^3(3x^4+5)^2

D)3x^3(3x^4+5)^2

E) 36x(3x^4+5)^2

So I know that I have to simplify the equation by multiplying what is inside the parenthesis to the power of 3, but I don't think I am doing it correctly. And I know once I figure that out I can take the second derivative from the first, that much I remember how to do.

So far for my simplifying I have gotten
3x^7+5^4
9x^7+5^4

both of which I know are wrong : ( I'm really frustrated with this step and even more frustrated knowing the next steps will be just as challenging. Any help would be appreciated. Thank you in advance : )
 
\(\displaystyle f(x) \ = \ (3x^{4}+5)^{3}\)

\(\displaystyle f'(x) \ = \ 3(3x^{4}+5)^{2}(12x^{3}) \ = \ 36x^{3}(3x^{4}+5)^{2}\)
 
steffyfee said:
If y = (3x^4 + 5)^3, then dy/dx = ?

I know that I have to simplify the equation No, you do not need to simplify anything.

by multiplying what is inside the [parentheses] to the power of 3 Your use of the phrase "by multiplying" is not correct.

The given expression tells us that the part inside the parentheses is "being raised" to the power of 3, not multiplied by some power of 3.

You do not need to expand this power. In other words, you do not need to calculate the following.

(3x^4 + 5)*(3x^4 + 5)*(3x^4 + 5)

Although, you could, if you wanted to, followed by differentiating the resulting polynomial term-by-term. I'm confident that this is not what your instructor wants to see.

To determine the first derivative of y, you are probably expected to apply the power rule and the chain rule, the results of which Glenn posted.

If you're not sure of these rule, look up the page numbers using your textbook's index, so that you can read about them. If you see something in your lessons that you do not understand, we welcome your specific questions.

Cheers ~ Mark 8-)
 
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