Differentiation (2 Viewers)

[skillstriker]

Differentiate y = a(x+b)² - 8, then find a and b if the parabola has tangent y=2x at the point P(4,8).

Full working please. Thanks!

 

[Carrotsticks]

 

[THE BEAST]

Yeh thats correct... i would have done it in the same manner.

 

[skillstriker]

Thanks Carrotsticks! Another question:

Differentiate x(4-9x^4)^4

 

[Carrotsticks]

 

[Timske]

Carrot it's -144x^4

 

[Carrotsticks]

Oh yes, I forgot to bring down the power. Thanks Timske =)

 

[skillstriker]

Carrotsticks your answer is correct (according to the Cambridge 2U textbook) but I can't find what's wrong in my working:

u = x
u' = 1
v = (4-9x^4)^4
v' = 4(4-9x^4)^3 multiplied by -36x^3 = -144x^3(4-9x^4)^3
y' = (4-9x^4)^4 -144x^4(4-9x^4)^3
y' = (4-9x^4)^3 (4-153x^4)

Is the answer in the textbook incorrect?

 

[Timske]

Carrotsticks your answer is correct (according to the Cambridge 2U textbook) but I can't find what's wrong in my working:

u = x
u' = 1
v = (4-9x^4)^4
v' = 4(4-9x^4)^3 multiplied by -36x^3 = -144x^3(4-9x^4)^3
y' = (4-9x^4)^4 -144x^3(4-9x^4)^3
y' = (4-9x^4)^3 (4-153x^4)

Your mistake lies in the 4th line, its x*[-144x^3(4-9x^4)^3] = -144x^4(4-9x^4)^3

 

[Timske]

Your mistake lies in the 4th line, its x*[-144x^3(4-9x^4)^3] = -144x^4(4-9x^4)^3

uv' + vu' = (x)*(-144x^3(4-9x^4)^3) + ((4-9x^4)^4)*(1)

 

[skillstriker]

Your mistake lies in the 4th line, its x*[-144x^3(4-9x^4)^3] = -144x^4(4-9x^4)^3

Thanks

 

[Timske]

Where did this x come from?

uv' + vu' , you left it out

 

[skillstriker]

^is my final answer still correct though? Also, the uv' was in the 5th not 4th line

 

[Timske]

lol your solution wasn't wrong afterall...

 

[Timske]

lol your solution wasn't wrong afterall...

EDIT:Actually it was wrong until you edited it.

y' = (4-9x^4)^4 -144x^3(4-9x^4)^3 = (4-9x^4)^3[4-9x^4 - 144x^3] how did you from here to
y' = (4-9x^4)^3 (4-153x^4)

lolz