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Differentiate to find dy/dx = 3x + 2;at point (-1,0) dy/dx = -1substitute in to y = mx + c, noting m = -1 and the line passes through (-1,0) yields c = -1y = -x - 1, simple to sketch this line.curve sketc...

RHS: cosh(x)cosh(y) + sinh(x)sinh(y) = 1/4(e^x + e^-x)(e^y + e^-y) + 1/4(e^x - e^-x)(e^y - e^-y) = 1/4(e^x.e^y + e^x.e^-y + e^-x.e^y + e^-x.e^-y + e^x.e^y - e^x.e^-y - e^-x.e^y + e^-x.e^-y) = 1/4(2e^x.e^y...

y = 12x^1/2 - x^3/2
First take the 1/2 power and multiply by the integer in front of the x (so 12 x 1/2 = 6), then minus 1 from the power (1/2 - 1 = -1/2) and replace the power ab...

We can find stationary points of functions by using differentiation, we start this by assessing each term individually, we start with the first term x², we first start by taking the power term ...

1/4xe^4x-1/16e^4x +c