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Lim((f(x+h)-f(x)))/h= lim(((x+h)² -x²)/h)=lim((h² +2xh)/h) as h tends to 0 the limit becomes 2x

a) f'(x)=2x-2-12x^1/2B)f'(x)=2+6x^-3/2c)f'(4)=0d) local minimum

The chain rule is a technique used when differentiating. It is needed when differentiating composite functions, i.e. when y = f(g(x)).For example, y = sin(x^3) is a composite function, where (referring to...

1)Separating variables. Firstly, we need to get the y terms all on the dy/dx side and the x terms on the other side. In this case, we divide both sides by y which gives (1/y)dy/dx = 1/(x+...

(1) is the equation y=x³+4x²-2x-3. First we want to find the coordinates of the curve for x=-4. This means that we are going to substitute x=-4 into (1) to find the value of y. y=(-4...