Can you differentiate y = (x^4 + x)^10
To solve this equation we will need to apply the chain rule. This states that:dy/dx = dy/du * du/dxTo make the question simpler, we shall let u = x4+ x, and so:y = u10 and u = x4+ xBoth of these equations can be differentiated to give:dy/du = 10u9 and du/dx = 4x3+ 1Using the chain rule formula written above, dy/dx = dy/du * du/dx = 10u9 * (4x3+ 1) = 10(4x3+ 1)(x4+ x)9
SA
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How do I differentiate y=x^x?
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 .