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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 f '(x) = [ 1 * (x-...
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Answered by Cosmin B. • Maths tutor
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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 following method: We choose eit...
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Answered by Cosmin B. • Maths tutor
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Solve (x + 2)(x+3) = (2x+4)

Expand: x 2 + 2x + 3x +6 = 2x+4 Take (2x+4) from both sides: x 2 +3x+2 = 0 Facorise: (x+2)(x+1) = 0 So solutions are x=-2 and x=-1
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Answered by Michael T. • Maths tutor
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∫ 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) = log(x). Ca...
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Answered by Michael T. • Maths tutor
49314 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) = 2lnx +2.
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Answered by Tom V. • Maths tutor
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