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How can we calculate the derivative of function f(x)= (x+2)/(x-1)?

In order to calculate the derivative of the given function, we need to apply the laws of derivation. Therefore:
f '(x) = ((x+2)/(x-1))'
f '(x) = [(x+2)' * (x-1) - (x+2) * (x-1)' ]/ (x-1)2

CB
Answered by Cosmin B. Maths tutor
5130 Views

How can we solve a two-equation, two-unknown values?

If we have two equations that look like this:
a1 * x + b1 * y = c1
and
a2 * x + b2 * y = c2
where x,y are variables and a1,a2,b1,b2 are coeficients.
then we solve it using the fol...

CB
Answered by Cosmin B. Maths tutor
5575 Views

Solve (x + 2)(x+3) = (2x+4)

Expand: x2 + 2x + 3x +6 = 2x+4
Take (2x+4) from both sides: x2+3x+2 = 0
Facorise: (x+2)(x+1) = 0
So solutions are x=-2 and x=-1

MT
Answered by Michael T. Maths tutor
8015 Views

∫ log(x) dx

Using "Integration by parts" or "reverse chain rule" .
Recall formula for intergration by parts: "∫f'(x) g(x) dx = f(x)g(x) - ∫f(x)g'(x)dx"
Then set f'(x) = 1, g(x)...

MT
Answered by Michael T. Maths tutor
48800 Views

Differentiate f(x) = 2xlnx.

Use the chain rule: f'(x) = v(du/dx) +u(dv/dx).

Let u = 2x, du/dx = 2, v = lnx, dv/dx = 1/x

Using this information: f'(x) = 2lnx + 2x/x

This simplifies to f'(x...

TV
Answered by Tom V. Maths tutor
22075 Views

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