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Recognise that the form this question is a circleRemember alternate circle equation (x + a)² + (x + b)² = r²Where centre of circle (-a,-b) and r is the radiusTo get the ri...

Use the chain rule as this is a composite function. Let u=2x+5.So the original equation becomes y=(u)^2.Using the chain rule: dy/dx = dy/du * du/dxdy/du = 2udu/dx = 2So dy/dx= 4uSince u=2x+5, dy/dx = 4(2x...

Rearranging gives:4cos(x)-1 = 2sin(x)tan(x) Substituting in tan(x)=sin(x)/cos(x) gives:4cos(x)-1 = 2sin(x)(sin(x)/cos(x))2sin²(x)=4cos²(x)-4cos(x)Substituting in 2sin^2<...

Given a circle in the general form you can complete the square to change it into the standard form.x² + 2gx + y² +2fy +c = 0 (1). General form of an equation which has the completing...

a) Integrate ln(x) by parts: u = ln(x), dv/dx = 1, du/dx = 1/x, v = x int(udv/dx) = uv - int(du/dx * v) = ln(x)/x - x so int(ln(x) + 1/x - x) = ln(x)/x - x + ln(x) + x^2 + Cb) y = ln(x)/x - x + l...