Find the derivative the following ways:
Using the Product Rule or the Quotient Rule. Simplify your result.
f(x) = (x - 1)(3x + 4)

Tangent lines Suppose f(2)=2 and f′(2) =3. Let g(x) = x²f(x) and h(x) = f(x) / x−3.

b. Find an equation of the line tangent to y = h(x) at x=2.

Given that f(1)=2 and f′(1)=2 , find the slope of the curve y=xf(x) at the point (1, 2).

Find the derivative the following ways:

Using the Product Rule or the Quotient Rule. Simplify your result.

f(x) = x(x-1)

Find the derivative the following ways:

Using the Product Rule or the Quotient Rule. Simplify your result.

g(t) = (t + 1)(t² - t + 1)

Find the derivative the following ways:

Using the Product Rule or the Quotient Rule. Simplify your result.

h(z) = (z³ + 4z² + z)(z - 1)

First and second derivatives Find f′(x),f′′(x).

f(x) = x/x+2

Derivatives from a table Use the following table to find the given derivatives. <IMAGE>

d/dx (f(x)g(x)) |x=1

Derivatives from graphs Use the figure to find the following derivatives. <IMAGE>

d/dx (f(x)g(x)) | x=4