Purchase Solution

Finding a derivative by implicit differentiation

Not what you're looking for?

Ask Custom Question

Question 3:
a) Find the derivative of the following functions dy/dx, by the method of implicit differentiation: i) (x^2)(y^2) - xy = 8; ii) sqrt(x + y) = x; iii) (x - y)/(2x + 3y) = 2x.

b) Find the equation of tangent line to the graph of the following function at the indicated points: i) y^2 - x^2 = 16; at (2, 2 sqrt(5); ii) (x^2)(y^3) - y^2 + xy - 1 = 0 at (1, 1).

Question 4:
a) Find the derivative of the following functions: i) f(x) = 4e^(3x+2) ... ii) f(x) = (x^3)(e^x); iii) f(x) = (x-1)e^3x+2; iv_ Find the second derivative of the function: f(x) = 2xe^3x.

b) i) find an equation of the tangent line to the graph of the function f(x) = xln, at; (1,1). ii) Find the equation of the tangent line to the graph of y = e^2x-3 at (3/2, 1).

Purchase this Solution
Solution Summary

Differentiating implicitly is modeled in an attached Word document.

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

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.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Implicit differentiation

    The process of finding the derivative of a function using implicit differentiation is examined, with three examples presented. The solution is presented in a PDF file.

  • differentiate and implicit differentiation

    ii) Use Implicit Differentiation to differentiate with respect to x. 4. Find the derivative for the following functions: a) y=(2x2-x)(3x2+5)8 b) y= this whole fraction is to have brackets around it.

  • Implicit Differentiation : Find Derivative y^2 = x^3

    So, Note that (see (2)), so we have ..................(3) Since , by (3), we have Implicit differentiation is used to find a derivative.

  • An Implicit Differentiation problem

    There is a very good reference on implicit differentiation: http://archives.math.utk.edu/visual.calculus/3/implicit.7/ Theory The slope of a line at a point is its first derivative evaluated at that point.

  • Derivatives and implicit differentiation

    107573 Derivatives and implicit differentiation Find the first and second derivative for for the next 2. z=2/(1+x^2) 3. f(x) = (x-1)/(x+1^2) find dy/dx by implicit differentiation 1. square root of (2x) + y^2 = 4 Please see the attached

  • Implicit differentiation

    107574 Find dy/dx by implicit differentiation Find dy/dx by implicit differentiation 1. (3x^2+1)^4 for this problems find d^2y/dx^2 1. y/x - x/y = 5 Please see the attached file. ________________________________________ find dy/dx by

  • Implicit Differentiation

    Implicit differentiation Implicit differentiation is a technique based on the Chain Rule that allows us to differentiate equations involving both independent and dependent variables.

  • First and Second Derivatives : Using Implicit Differentiation

    0---------------second derivative Implicit differentiation is investigated.

  • implicit differentiation

    This solution is comprised of a detailed explanation to use implicit differentiation to find the slope of the tangent line to the curve at the point .

View More Related Solutions