3. Techniques of Differentiation

Find and simplify the derivative of the following functions.

h(x) = (5x⁷ + 5x)(6x³ + 3x² + 3)

7–14. Find the derivative the following ways:

a. Using the Product Rule (Exercises 7–10) or the Quotient Rule (Exercises 11–14). Simplify your result.

y = x² - a² / x-a, where a is a constant

7–14. Find the derivative the following ways:

a. Using the Product Rule (Exercises 7–10) or the Quotient Rule (Exercises 11–14). Simplify your result.

y = x² - 2ax +a² / x-a, where a is a constant

Product Rule for three functions Assume f, g, and h are differentiable at x.

b. Use the formula in (a) to find d/dx(e^x(x−1)(x+3))

9–61. Evaluate and simplify y'.

y = (2x−3)x^3/2

Finding derivatives from a table Find the values of the following derivatives using the table. <IMAGE>

c. d/dx ((f(x)g(x)) |x=3

7–14. Find the derivative the following ways:

a. Using the Product Rule (Exercises 7–10) or the Quotient Rule (Exercises 11–14). Simplify your result.

f(w) = w³ -w / w

7–14. Find the derivative the following ways:

a. Using the Product Rule (Exercises 7–10) or the Quotient Rule (Exercises 11–14). Simplify your result.

g(s) = 4s³ - 8s² +4s / 4s

Find an equation of the line tangent to the given curve at a.

y = (x + 5) / (x - 1); a = 3

Use a graphing utility to graph the curve and the tangent line on the same set of axes.

y = (x + 5) / (x - 1); a = 3

Find an equation of the line tangent to the given curve at a.

y = 2x² / (3x - 1); a = 1

Use a graphing utility to graph the curve and the tangent line on the same set of axes.

y = 2x² / (3x - 1); a = 1

Derivatives Find and simplify the derivative of the following functions.

g(x) = e^x / x²-1

Derivatives Find and simplify the derivative of the following functions.

g(w) = √w+w / √w-w

Derivatives Find and simplify the derivative of the following functions.

h(w) = w⁵/³ / w⁵/³+1