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To get dy/dx from a formula y in terms of x we must differentiate y with respect to x. Generic formula for term differentiation: d/dx(ax^b) = bax^b-1 = times the coefficient by the power and minus the pow...

Before we get started with answering the question, it is generally good practice to write down any formulas and equations you know that will help us work through the solution. So what formula do we know t...

-cos(2x)/(x²) - 2sin(2x)/(x)

For questions like these it's easier to first rewrite z as z=x+iy. 

Once we plug this back into the original equation we get x-iy-i = 2ix-2y+1

Rearranging both sides to group together the re...

Find dy/dx

Remember quotient rule dy/dx=(u'v-v'u)/v^2

u=4x       u'=4

v=x^2+5         v'=2x

dy/dx=(20-4x^2)/(x^2+5)^2 (simplified)