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dy/dx = 4/(x^2+5) - 4x(2x)/(x^2+5)dy/dx= 4(5-x^2)/(x^2+5)^2Part B4(5-x^2)/(x^2+5)^2<05-x^2<05<x^2

First we need to use the factor theorem to find a factor.f(1)=-25 so x-1 is not a factorf(-1)=9 so x+1 is not a factorf(2)=0 so x-2 is a factorSo x-2 is our starting point, we need to polynomial division ...

To solve these equations you first want to eliminate the same variable from each equation. In this question it is easiest to eliminate Y, to do this we will times equation 1 by 3 to get 21X-18Y=114 and eq...

Change 16 as a power of 2 to get 2⁴. Change 8^2x as a power of 2 gives (2³)^2x. You can times the two powers together giving 2^6x.So 16*8^2x=2...

Step 1 differentiate substitution: du/dx = -2sin(2x)Step 2 rearrange for dx: dx=du/-2sin(2x)Step 3 substitute: integral= ∫u²sin³(2x).du/-2sin(2x)Step 4 get the integral in terms of u...