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Let u = x²+4x+2 so y = ln(u).

Then dy/du = 1/u and du/dx = 2x+4.

Using the chain rule we have:

dy/dx = (dy/du)*(du/dx)

= (1/u)*(2x+4)

= (2x+4)/(x²+...

These problems can be tricky as they use unfamiliar trigonometric functions such as secant and cosecant. It is much easier to approach these problems by replacing these trigonometric functions with more f...

We know from simple fraction rules that dy/dx=(dy/dt)/(dx/dt). dy/dt=2t, dx/dt=3t^2+1. Therefore, dy/dx=2x2/12+1=4/13

We would do this by differentiating everything individually so to differentiate x² we multiply the x² by the power which is 2 and then take the power down by 1 to make 2x. To differe...

Let a=60 and b=300.

Then cos(a)=cos(60)=0.5 and cos(b)=cos(300)=0.5, therefore cos(a)=cos(b).

Then sin(a)=sin(60)=sqrt(3)/2 and sin(b)=sin(300)=-sqrt(3)/2, therefore sin(a)=sin(b) is incorre...