Differentiate y= (6x^2 - 5)^(3/2) with respect to x
Simplify the equation to y=u3/2 where u = 6x2 -5Use the chain ruledy/dx = dy/du x du/dxdy/du = (3/2)u1/2du/dx = 12x - 0Therefore dy/dx = (3/2)u1/2 x 12xBut u = 6x2-5 so substitute that into the derivative.dy/dx = 3/2(6x2-5)1/2 x 12xSimplify to dy/dx= 18x(6x2-5)1/2
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All answers ▸Differentiate y = 5x^3 + 7x + 3 with respect to x
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Let w, z be complex numbers. Show that |wz|=|w||z|, and using the fact that x=|x|e^{arg(x)i}, show further that arg(wz)=arg(w)+arg(z) where |.| is the absolute value and arg(.) is the angle (in polar coordinates). Hence, find all solutions to x^n=1 .