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Using first principles find the differential of x^2

Lim ((f(x+h)-f(x)))/h= lim(((x+h) 2 -x 2 )/h)=lim((h 2 +2xh)/h) as h tends to 0 the limit becomes 2x
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if f is defined on with f(x)=x^2-2x-24(x)^0.5 for x>=0 a) find 1st derivative of f, b) find second derivative of f, c) Verify that function f has a stationary point when x = 4 (c) Determine the type stationary point.

a) f'(x)=2x-2-12x 1/2 B)f'(x)=2+6x -3/2 c)f'(4)=0d) local minimum
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What is the chain rule?

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 th...
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Find the general solution to the differential equation dy/dx = y/(x+1)(x+2)

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)(x+2). 2) To make ...
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Find the equation of the tangent to the curve y=x^3 + 4x^2 - 2x - 3 where x = -4

(1) is the equation y=x 3 +4x 2 -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) 3 + 4(-4) 2 - 2(-4)...
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