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y=x²dy/dx= Lim_h-->0( ((x+h)²-x²) / (x+h-x) )dy/dx= Lim_h-->0( (x² + 2hx + h² - x²) / h )dy/dx= Lim_h-->0...

First, we should look at the laws of logarithms.log_ax+log_ay=log_axylog_ax-log_ay=log_a(x/y)klog_ax=log_ax^kWe ca...

y=x^x, taking natural log of both sides
ln(y)=ln(x^x), using laws of logs
ln(y)=xln(x), using product rule and implicit differentiation
dy/dx 1/y=ln(x)+1
dy/dx=(ln(x)+1)y
dy/dx=(l...

consider the discriminant b²-4ac 8²-4x1x17 64-68=-4 discriminant is below 0, there are no real roots therefore x² - 8x +17 <0

f’(x)= 9x^3+4x