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The first step in solving this question is to differentiate equation y with respect to x. To differentiate a given 'x' term in an equation use the following method --> xⁿ becomes nx^(n-1...

dy/dx= 2x+2 , gradient is equal to 1 so dy/dx also equals 1.1=2x+2-1=2xx=-1/2plug this value of x into the equation to get y=17/4

Let u= 8x then du/dx = 8Let v= cos(3x) then dv/dx = -3sin(3x)Therefore using the product rule: dy/dx = (cos(3x))(8) + (8x)(-3sin(3x))So dy/dx = 8cos(3x) - 24xsin(3x) .

Firstly we need to find the stationary point on the curve. We know what at a stationary point the gradient is zero so we will find the gradient of the curve. We do this by differentiation, when we have di...

Integration by parts should be used when you want to integrate a function composed of two factors (we can call them 'u' and 'dv'), where it is fairly easy to derive 'u', while it is difficult or impossibl...