Search over 10,000 free study notes

First, we differentiate y = x^2 + 3x + 2 to find the slope of the curve at any given x point:

dy/dx = 2x + 3

So at x = 1, dy/dx = 2 + 3 = 5

We know that straig...

Using the chain rule with u = 2x:

y = sin(2x) becomes y = sin(u)

dy/dx = dy/du * du/dx

dy/du = cos(u)

du/dx = 2

So dy/dx = dy/du * ...

Definite integrals produces a numerical answer. It is asking the question: what is the area under the curve f(x) between x=a and x=b.

Indefinite integrals produces a function. It is askin...

Firstly, what is the product rule? What does it actually say? Well, it tells us how to differentiate a function of the form uv - the product of the functions u and v. If y = u...

Hint: the chain rule states that for y=u(x) ^a, the derivative will be dy/dx = dy/du * du/dxSo we just need to find dy/du and du/dx!In this case u(x)=x-3, so du/dx = 1.from y=u^(-3), dy/du = -3u^(-4).This...