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How would you derive y = function of x; for example: y = 3x^3 + x^2 + x

The best way to remember derivatives is to use algebra, and the general function is y = ax n -> dy/dx = anx n-1 So for this equation dy/dx = (3x3)x 3-1 + (2x1)x 2-1 + 1x 1-1 So the answer would be dy/dx =...
GA
Answered by George A. • Maths tutor
3706 Views

How do you solve quadratic inequalities?

Quadratic inequalities generally don't arrive in the standard quadratic form (Ax^2 + Bx +c) and so can be sometimes difficult to spot. However, if you see an X^2 - or brackets that expand to X^2 - on either ...
DK
Answered by David K. • Maths tutor
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Factorise and solve x2 - 8x + 15 = 0

Factorise the quadratic into two brackets to make (x-3)(x-5)=0 Because the product of these brackets is zero then the value of one of the brackets must equal zero. In order for one of the brackets to have a ...
MS
Answered by Mohamed S. • Maths tutor
9434 Views

Expand and simplify (x+2)(x+3)

Use the FOIL method to remember which components you need to multiply together. F = F irst two, O = O utside two, I = I nside two, L = L ast two. Then add your answers together and collect like terms to simp...
NS
Answered by Natasha S. • Maths tutor
58407 Views

Find the gradient of the curve y = x^2(ln(x)) at x = e

We'll need to use the product rule. Let's take u = x^2 -> du/dx = 2x, and v = ln(x) -> dv/dx = 1/x Then dy/dx = x^2(1/x) + 2xln(x) = x + 2xln(x) Substituting our x value gives (dy/dx)|(x = e) = e + 2el...
CR
Answered by Charlie R. • Maths tutor
7246 Views