Calculus I Assignment # 2

This assignment covers

Derivatives with power, product, quotient and chain rule

Implicit Differentiation

Higer Order Derivatives

QUESTIONS

A) Find the first derivative

 1) 2) 3) 4) 5) f (x) = sin 2 (4x 3) 6)

.

B) Use implicit differentiation to find the derivative

 1) 5x 3 - 2x 2 y 2 + 4y 3 - 7 = 0 2) 3x 2 - x y 2 + y - 1 = 1 3) xy 2 = sin (x + 2y)

.

C)

1) Find equations of the tangent and normal lines to x 2 y - y 3 = 8 at P(-3, 1)

2) Find the first, second and third derivative of y = 5x 3 + 4x 1 / 2

.

SOLUTIONS

A) Find the first derivative

 .1) 2) 3) 4) 5) f '(x) = 24x 2 sin (4x 3)cos (4x 3) 6)

.

B) Use implicit differentiation to find the derivative

 1) 15x 2 - 4xy 2 - 4x 2 yy' + 12y 2 y' = 0factor out y', transpose and divide to get 2) to simplify, multiply through by y 2. 3)

.

C)

1) 2xy + x 2 y' -3y 2 y' = 0

we solve for y' and substitute x = -3, y = 1

The equation of the normal line with slope = -1 is y = -x -2.

.

2)

 y' = 15x 2 + 2x - 1 / 2 y'' = 30x - x - 3 / 2 y''' = 30 + (3/2) x - 5 / 2

.

.

.

(all content of the MathRoom Lessons © Tammy the Tutor; 2002 - 2005).