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y=x 2 dy/dx= Lim h-->0 ( ((x+h) 2 -x 2 ) / (x+h-x) )dy/dx= Lim h-->0 ( (x 2 + 2hx + h 2 - x 2 ) / h )dy/dx= Lim h-->0 ( (h 2 + 2hx) / h )dy/dx= Lim h-->0 ( h + 2x )dy/dx= Lim h-->0 ( h ) + 2xd...

First, we should look at the laws of logarithms.log a x+log a y=log a xylog a x-log a y=log a (x/y)klog a x=log a x k We can see that laws 1 and 3 might be helpful, so we simplify our equation.log 2 2 4 +log...

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=(ln(x)+1)x^x

consider the discriminant b 2 -4ac 8 2 -4x1x17 64-68=-4 discriminant is below 0, there are no real roots therefore x 2 - 8x +17 <0

f’(x)= 9x^3+4x