Differentiation

[Yunie]

Differentiate with respect to x:

(x^2 + 2)/ square root 2


I would greatly apprectiate it if anyone could help me with this question. I have tried to do it but to no avail. Please help me with this single question and hopefully I will understand it and be able to do the other differentiation questions.

Thanks.

[eranga262154]

The answer is,

2x/sqrt(2).

Need just only basis as follows,

1.) d(xⁿ)/dx = nx^(n-1)
2.)) Differentiation of a constant is zero.

[Code Doc]

In general: The derivative of a fraction is "the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator."

Therefore, your derivative is
[(Sqrt 2)(2x) - 0] / 2 = x(Sqrt 2)

[tendemo]

Another aproach,
Let U = x^2 + 2 and V = 2 ^ (-1/2)
Then Let dU = 2x and dV = 0

From (VdU - Udv)/ V^2

We get (Sqrt2.2x - (x^2 + 2)(0))/ (Sqrt2)^2
giving 2x(sqrt2)/ (sqrt2) ^2
2x(sqrt2)/2
x(sqrt2)

[VBAhack]

I think there is a much simpler way to look at this.

y = (x² + 2)/√2
y = x²/√2 + 2/√2
y = ax² + b

y' = 2ax = 2x/√2

[Yunie]

Hey guys, thanks for your help. I do know the steps of the differentiation, but the problem I am facing is to solve the question completely.

I am stucked while doing the question...

See here:

y = (x^2 + 2)/ √x
= (x^2 +2)/ (x^1/2)
dy/dx = [(x^1/2* 2x) - x^2 + 2* 1/2x^(-1/2)] / (x^1/2)^2
.....


After that, I don't know how to continue...I really hate the (1/2) thingy, it's so confusing especially when doing differentiation type of question..

Sorry to trouble you guys..

[Yunie]

The answer is (3 √x/2) - (1/ √x^3)

[krtxmrtz]

It's easier if you calculate the derivative of a sum than that of a quotient. So, write it as:

f(x) = (x² + 2) / x^1/2 = x^3/2 + 2x^-1/2

Now, apply the rule to each addend,

f'(x) = 3/2 x^1/2 - x^-3/2

[eranga262154]

It's easier if you calculate the derivative of a sum than that of a quotient. So, write it as:

f(x) = (x² + 2) / x^1/2 = x^3/2 + 2x^-1/2

Now, apply the rule to each addend,

f'(x) = 3/2 x^1/2 - x^-3/2

You are 100% correct.

For the different situation we should you much simpler approches. First it should make in simpler form as much as possible, and go further and do your calculations.