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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...

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)

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) = ...

2x + 5 lnx

U_n+1=1/U_n where U₁= 2/3First of all, we need to find U₂ and U₃ and so on, up until we notice a pattern in the answers. U₂ = 1/(2/3) = 3/2U...