Calculus - Derivatives and Numerical Values
Not what you're looking for?
Need help with calculus homework problems.
In Exercises 41-48, find dy/dx
44. 5x 4/5 + 10y 6/5 = 15
____________________________________________________________________
54. a. By differentiating x 2 - y2 =1 implicitly, show that dy/dx = x/y
b. Then show that d2y/dx2 = - 1/y3.
_____________________________________________________________________
Numerical Values of Derivatives
56. Suppose that the function f(x) and its first derivative have the following values at
x = 0 and x = 1
x f(x) f'(x)
0 9 -2
1 -3 1/5
Find the first derivatives of the following combinations at the given value of x
a. f(x), x = 1
b. , x = 0
c. f , x =1
d. f(1 - 5 tan x), x = 0
e. f(x) , x = 0
2+cosx
f. 10sin f2(x), x = 1
62. If x1/3 + y1/3 = 4, find d2y/dx2 at the point (8,8)
68. For what value or values of the constant m, if any is
f(x) =
a. continuous at x = 0?
b. differentiable at x = 0?
Give reasons for your answers
Purchase this Solution
Solution Summary
The derivatives and numerical values in calculus are determined. Complete, Neat and Step-by-step Solutions are provided in the attached file.
Solution Preview
The solution file is attached.
In Exercises 41-48, find dy/dx
44. 5x 4/5 + 10y 6/5 = 15
5(4/5) x^(-1/5) + 10(6/5) y^(1/5) (dy/dx) = 0
4 x^(-1/5) + 12 y^(1/5) (dy/dx) = 0
dy/dx = -4 x^(-1/5) / 12 y^(1/5) = -1/[3 (xy)^(1/5)]
54. a. By differentiating x 2 - y2 =1 implicitly, show that dy/dx = x/y
b. Then show that d2y/dx2 = - 1/y3.
(a) 2x - 2y(dy/dx) = 0
dy/dx = 2x/2y = x/y
(b) d^2y/dx^2 = [y - x(dy/dx)]/y^2
= [y - x(x/y)]/y^2
= [y^2 - x^2]/y^3
= -1/(y^3)
Numerical Values of Derivatives
56. Suppose that the function f(x) and its first derivative have the following values at
x = 0 and x = ...
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.