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1. Find dy/dx of y=(2x+3)(x+5)^2
Okay, so I'm using product rule and this is what i've done so far:

(2x+3)(x+5)^2
2 [x+5]^2 + 2x+3 (2) (x+5) (1)
=2 [x+5]^2 + 2*2x+3 (x+5)

What do I do next, show the steps please?
2. (Original post by Nkhan)
Find dy/dx of y=(2x+3)(x+5)^2
Okay, so I'm using product rule and this is what i've done so far:

(2x+3)(x+5)^2
2 [x+5]^2 + 2x+3 (2) (x+5) (1)
=2 [x+5]^2 + 2*2x+3 (x+5)

What do I do next, show the steps please?
There are a number of ways you could do this. You could expand the 3 brackets and then it'd just be straight differentiation of a polynomial. You could use the product rule

Where

and

Or you could do the product rule of 3 functions.

Where

and

A lot of people seem to forget to apply the chain rule, so the best method to ensure you do it correctly would be either to multiply it all out, or the last method, product rule of 3 functions.

Could you rewrite what you've got up to? What you have done seems to be correct, although don't forget you're multiplying the 2 from the with the entire function, not just the 2x ( you didn't put brackets around it).
3. 2(x+5)^2 + 2(2x+3)(x+5)

2(x+5)[x+5+2x+3]

2(x+5)(3x+8)
4. (Original post by Noble.)
There are a number of ways you could do this. You could expand the 3 brackets and then it'd just be straight differentiation of a polynomial. You could use the product rule

Where

and

Or you could do the product rule of 3 functions.

Where

and

A lot of people seem to forget to apply the chain rule, so the best method to ensure you do it correctly would be either to multiply it all out, or the last method, product rule of 3 functions.

Could you rewrite what you've got up to? What you have done seems to be correct, although don't forget you're multiplying the 2 from the with the entire function, not just the 2x ( you didn't put brackets around it).
Okay thanks And yeah the simplifying but is the difficult bit for me, I just dont no when and what to cancel out :|
But thanks for ur help
5. (Original post by Pheylan)
2(x+5)^2 + 2(2x+3)(x+5)

2(x+5)[x+5+2x+3]

2(x+5)(3x+8)
How did you cancel out? what bits cancelled out each other? Thats the hardest part for me :|
6. (Original post by Nkhan)
How did you cancel out? what bits cancelled out each other? Thats the hardest part for me :|
factorise 2(x+5) from both terms, this leaves you with x+5 in the first term and 2x+3 in the second. x+5+2x+3 = 3x+8
7. (Original post by Nkhan)
Okay thanks And yeah the simplifying but is the difficult bit for me, I just dont no when and what to cancel out :|
But thanks for ur help

You can take out a factor of 2 and from both.

8. (Original post by Pheylan)
factorise 2(x+5) from both terms, this leaves you with x+5 in the first term and 2x+3 in the second. x+5+2x+3 = 3x+8
Ahh right, thanks so much

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