Mathematics OpenStudy (anonymous):

How to apply the product rule in differentiation, Please see the attached image file for the question: I am not understanding the 3rd part of this solution. OpenStudy (anonymous): OpenStudy (phoenixfire):

The third part just substitute values for u, dv/dx, v, and du/dx and then proceeded to expand and simplify. OpenStudy (anonymous):

I am not getting this one: How did we get this? If simplification how can I do it. I am not good at simplification. $(2x^2+6x)(6x^2+10x)+(2x^3+5x^2)(4x+6)$ OpenStudy (anonymous):

How did we got this 2x^2 ? OpenStudy (phoenixfire):

$u=2x^2 + 6x$ $v=2x^3+5x^2$ use differentiation rule to find the derivatives: ${dy \over dx}=ax^{a-1}$ ${du \over dx}=4x+6$ ${dv \over dx}=6x^2+10x$ then substitute these values into the product rule equation: ${dy \over dx} = u{dv \over dx} + v{du \over dx}$ OpenStudy (anonymous):

Thank you, I understood this part .. can you please tell me what next we have to do? OpenStudy (phoenixfire):

After substituting you get this... $(2x^2+6x)(6x^2+10x) + (2x^3+5x^2)(4x+6)$ then you expand the brackets and simplify. giving you: $20x^4+88x^3+90x^2$ OpenStudy (anonymous):

In first part, it is cross multiplication, if I am right? In second part of simplification How did we got this 20x^4 ... and so on? its confusing OpenStudy (phoenixfire):

(2x^2 * 6x^2) + (2x^2 * 10x) + (6x * 6x^2) + (6x * 10x) + (2x^3 * 4x) + (2x^3 * 6) + (5x^2 * 4x) + (5x^2 * 6) (a + b)(c + d) = ac + ad + bc + bd OpenStudy (anonymous):

ok got it .. and please tell me the last part :) OpenStudy (phoenixfire):

well that was the expansion of brackets... now simplify the equation by combining like-terms. for example: 10x^2 + 3x^2 becomes 13x^2 because the x^2 is common. OpenStudy (anonymous):

Sorry, still not getting it. I have took a lot of your time. If you can please provide me a link where I can understand the simplification process easily because I need to clear this concept of simplification for solving differentiation. OpenStudy (phoenixfire):

well I'll do the first part, then you can do the second. (2x^2+6x)(6x^2+10x)=(2x^2 * 6x^2) + (2x^2 * 10x) + (6x * 6x^2) + (6x * 10x) do each term 2x^2 * 6x^2 = 12x^4 (ax^b * cx^d)=(ac)x^(b+d) 2x^2 * 10x = 20x^3 6x * 6x^2 = 36x^3 6x * 10x = 60x^2 put them all together 12^4 + 20x^3 + 36x^3 + 60x^2 combine like-terms: 20x^3 + 36x^3 = 56x^3 ax^c + bx^c = (a+b)x^c giving you 12x^4 + 56x^3 + 60x^2 now you go try the second half (the last four parts of the expansion) then combine the terms with mine, and you should arrive at the answer

Latest Questions babygirlcuhh: All praise is due to ALLAH alone, Lord of all the worlds... THEE alone do we worship and THEE alone do we implore for health.
34 minutes ago 2 Replies 0 Medals BBlove2020: Which colonial group was formed first? (5 points) First Continental Congress Comm
1 hour ago 0 Replies 0 Medals doosii: What is the mass in grams of KBr in 0.400 L of a .350 M solution?
1 hour ago 0 Replies 0 Medals hannahcarrafa045: Dependent variables can be the result of more than one independent variable. Consider your phone bill as presented in the Opening Activity.
1 hour ago 0 Replies 0 Medals KIYAMAYQXW: Marlena created a table of values u200bu200brepresenting the height in feet, h ( t ), of a coconut falling to the hard ground with a height of 0 feet, colle
1 hour ago 0 Replies 0 Medals Greatkitty2418: A society in the near future values education and career over family more and mor
1 hour ago 0 Replies 0 Medals KIYAMAYQXW: Marlena created a table of values u200bu200brepresenting the height in feet, h ( t ), of a coconut falling to the hard ground with a height of 0 feet, colle
1 hour ago 0 Replies 0 Medals itslillyy: What is the overall effect of Jefferson's nuanced word choices in the declaration
1 hour ago 0 Replies 0 Medals itslillyy: lol idk
1 hour ago 0 Replies 0 Medals gpman: quadrilaterals LMNO and PQRS Translate PQRS so that point P of PQRS lies on point L of LMNO, then dilate PQRS by the ratio segment LM over segment PQ.
2 hours ago 0 Replies 0 Medals