Calculus Question (1 Viewer)

[Getteral09]

hey everyone, hope u guys have a great holiday!

I have a calculus question which i need help on. Here it is:

Differentiate
a) 2/x^4 + 1/5x^2



Thanks heaps,


From Getteral

 

[alexvincent]

<SUP></SUP><?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o>d/dx [2/x<SUP>4</SUP> + 1/5x<SUP>2</SUP>] = 2x<SUP>-4</SUP> + x<SUP>-2</SUP>/5<o></o>
= -4.2.x<SUP>‑5</SUP> + -2.x<SUP>-3</SUP>/5<o></o>
= -8x<SUP>-5</SUP> – 2x<SUP>‑3</SUP>/5<o></o>
= -8/x<SUP>5</SUP> – 2/5x<SUP>3</SUP><o></o>

Knowing your index laws is very important.</o>

 

[Riviet]

d/dx (2/x⁴ + 1/5x²) = d/dx (2x^-4 + 5x^-2)
= (-4)(2)x^-5 + (-2)(5)x^-3
= -8x^-5 - 10x^-3
= -8/x⁵ - 10/x³

edit: 1/5x² was a bit ambiguous. If you meant x²/5, see alexvincent's answer, if you meant 1/(5x²), see my answer.

 

[Getteral09]

Hey can anyone please explain to me this calulus question: 2x(3x^4-x) using the product rule?


Thanks,

From Getteral

 

[airie]

Hey can anyone please explain to me this calulus question: 2x(3x^4-x) using the product rule?


Thanks,

From Getteral

This is the product of 2x and 3x⁴-x. The derivative of 2x is 2, and that of 3x⁴-x is 12x³-1.

So, by using the product rule, the derivative of the whole expression is 2(3x⁴-x) + 2x(12x³-1) = 30x⁴-4x

 

[Getteral09]

Hep Peeps! can anyone please explain to me this calulus equation using the qoutient rule? Here is the equation: 3x+1/sqrt(x+1)

 

[twilight1412]

Hep Peeps! can anyone please explain to me this calulus equation using the qoutient rule? Here is the equation: 3x+1/sqrt(x+1)

quotient rule
u = top
v = bottom
' = derivative

vu' + uv'
-----------
v^2

to get the derivatives you may need to combine rules in your case the chain rule for the bottom ><

 

[Getteral09]

Wat answer did you get?

 

[sando]

let me guess.. you just started yr 12 maths and this is going to be ur homework thread

 

[airie]

Or Getteral09 might be in year 10 or lower and just trying to learn more maths than that taught at school

 

[SoulSearcher]

Or Getteral09 might be in year 10 or lower and just trying to learn more maths than that taught at school

I doubt that

 

[airie]

I doubt that

... Why?

Is it because, it's, erm, MATHS, and everyone gets enough of it at school already?