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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) .

A standing wave is the interference of two sinusoidal waves travelling in opposite directions, confining the wave and its energy to a fixed position, creating nodes and anti nodes .
nodes - points w...

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...