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differentiate x^3-6x^2+2x=0

To differentiate an equation, the first step is multiplying the coefficients of the variables (the coefficient is the number a variable is already being multiplied by, for example in 6x the coefficient of th...
MK
Answered by Meg K. • Maths tutor
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Find the two real roots of the equation x^4 -5=4x^2 Give the roots in an exact form.

Disguised quadratic. Let y=x^2So quadratic become y^2-4y-5=0so (y-5)(y+1)=0so y=5 and y=-1so x^2 = 5 or -1cannot be -1 as not real henso x^2=5x=+-sqrt(5)
RJ
Answered by Rishi J. • Maths tutor
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A curve is defined by the parametric equations x = 3^(-t) + 1, y = 2 x 2^(t). Show that dy\dx = -2 x 3^(2t).

Write 3^(t) as an expression involving x : We can rewrite x = 3^(-t) + 1 as x - 1 = 3^(-t) ; equivalently, 3^(t) = (x-1)^(-1). Substitute this expression into y, to write y in terms of x: y = 2 x 3^(t) = 2 x...
MK
Answered by Maleeha K. • Maths tutor
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differentiate the function (x^2 +5/x + 3) with respect to x

2x + 5 lnx
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A sequence is defined as: U(n+1) = 1/U(n) where U(1)=2/3. Find the sum from r=(1-100) for U(r)

U n+1 =1/U n where U 1 = 2/3First of all, we need to find U 2 and U 3 and so on, up until we notice a pattern in the answers. U 2 = 1/(2/3) = 3/2U 3 = 1/(3/2) = 2/3As we can see, U 1 and U 3 are equal, and s...
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