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First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing...

dy/dx = 24e^6x - sin(x) + 6

Firstly, solving simultaneous equations finds the point(s) where two lines on a graph meet. They can either be two linear equations (finding one point of intersection), a linear and a quadratic (can have ...

2cosx - sinx = Rcos(x+a) = Rcos(x)cos(a)-Rsin(x)sin(a)

Implying

2cos(x)=Rcos(x)cos(a)

Rcosa = 2

Similarly: Rsin(a) = 1

Therefore tan(a) = 1/2

Meaning a=26.57 Degr...

To find velocity you differentiate displacement with respect to time

Therefore ds/dt = v = (3x2)t²-(12x2)t²+7

Implying v = 6t²-24t+7