The Power Rule
- Thread starter kidmo87
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mmm4444bot
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I see an arithmetic mistake in your calculation of d/dx[2x^2 + 3x]. Two times two is four, not six.
You forgot to type the exponent 4, on the next to the last line. Otherwise, you correctly applied the Power and Chain rules.
I would submit the factored version: 5(4x + 3)(2x^2 + 3x)^4
Otherwise, if you desire to multiply out stuff, then expand everything and combine all like-terms (yuck).
Btw, it's not correct to write at the onset that f`(x) equals 5(2x^2 + 3x)^4 because it does not. I understand you were not finished at that point, but it's still an incorrect equation to write down.
Cheers :cool:
You forgot to type the exponent 4, on the next to the last line. Otherwise, you correctly applied the Power and Chain rules.
I would submit the factored version: 5(4x + 3)(2x^2 + 3x)^4
Otherwise, if you desire to multiply out stuff, then expand everything and combine all like-terms (yuck).
Btw, it's not correct to write at the onset that f`(x) equals 5(2x^2 + 3x)^4 because it does not. I understand you were not finished at that point, but it's still an incorrect equation to write down.
Cheers :cool:
Do not get sloppy.
\(\displaystyle Given\ y = (2x^2 + 3x)^5\)
\(\displaystyle Let\ u = 2x^2 + 3x \implies y = u^5\ and\ \dfrac{du}{dx} = 4x + 3\ and\ \dfrac{dy}{du} = 5u^4\implies\)
\(\displaystyle \dfrac{dy}{dx} = \dfrac{dy}{du} * \dfrac{du}{dx} = 5u^4 * (4x + 3) = (20x + 15)( 2x^2 + 3x)^4.\)