Maths differentiation using product rule

Hi, I've been trying to figure out dy/dx of x(1+3x)⁵but to no avail! I've tried but came out with the wrong answer, I tried:

u=x v=(1+3x)⁵
u'=1 v'=5(1+3x)⁴(multiplied by 3)

dy/dx= 5x(1+3x).(3)+(1+3x)⁵However I know that this is incorrect, and that the answer is (1+18x)(1+3x)⁴

Does anybody know how to do this? Any help at all would be greatly appreciated!!!

Reply 1

james22

16

You missed a power of 4 in your dy/dx, but assuming this is a typo you can try factoring out a common factor.

Reply 2

HandmadeTurnip

17

~~You've differentiated v wrong, you need to use the chain rule.~~

EDIT: Sorry, I've just noticed you multiplied by the 3 afterwards. As other's have said, you've just forgotten to include the power of 4.

(edited 9 years ago)

Reply 3

Underthecandle

1

You've almost got it. The power of 4 from the v' has disappeared in the dy/dx line, once that goes back in try factorising what you have

Reply 4

Rbutton

OP

13

Original post by james22

You missed a power of 4 in your dy/dx, but assuming this is a typo you can try factoring out a common factor.

Yeah, that was a typo, sorry. In the answer only one of the two products has a power though and both of mine did, factoring wouldn't remove the power would it?

Reply 5

flyingraccoon

1

Original post by Rbutton

Hi, I've been trying to figure out dy/dx of x(1+3x)⁵but to no avail! I've tried but came out with the wrong answer, I tried:

u=x v=(1+3x)⁵
u'=1 v'=5(1+3x)⁴(multiplied by 3)

dy/dx= 5x(1+3x).(3)+(1+3x)⁵However I know that this is incorrect, and that the answer is (1+18x)(1+3x)⁴

Does anybody know how to do this? Any help at all would be greatly appreciated!!!

u=x v=(1+3x)⁵
u'=1 v'=15(1+3x)⁴

15x(1+3x)⁴ + (1+3x)⁵

You can take out a common factor of (1+3x)⁴
This leaves (1+3x)⁴ (15x + 1 + 3x)
Simplify for the answer you want

Reply 6

james22

16

Original post by Rbutton

Yeah, that was a typo, sorry. In the answer only one of the two products has a power though and both of mine did, factoring wouldn't remove the power would it?

Take out a factor of (1+3x)^4.

Reply 7

Rbutton

OP

13

Original post by flyingraccoon

u=x v=(1+3x)⁵
u'=1 v'=15(1+3x)⁴

15x(1+3x)⁴ + (1+3x)⁵

You can take out a common factor of (1+3x)⁴
This leaves (1+3x)⁴ (15x + 1 + 3x)
Simplify for the answer you want

Oohhhhhh, I see how it works now. Thank you so much!