Purchase Solution

Derivatives: Chain Rule

Not what you're looking for?

Ask Custom Question

Please see the attached file for the fully formatted problems.

For a composite function f(x) = g(u(x)) state the chain rule for the derivative f(x).
For each of the following functions, compute the derivative, simplifying your answers.
f(x)=ln(1 + x^2)
f(x)= sin(x^2)
f(x) = (sin x)^2

(a) For a composite function f(x) = g(ti(x)), state the chain rule for the derivative of f (x). For each of the following functions, compute the derivative, simplifying your answers:
(b) f(x) = in(1 + x2) (c) f(x) = sin(x2) (d) (x) = (sin x)2

Purchase this Solution
Solution Summary

Derivatives are found using the Chain Rule. The composite functions for chain rules for The derivatives are given.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

a)

Chain rule ...

Purchase this Solution
Free BrainMass Quizzes
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.

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.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Use chain rule for the first three derivatives of cos^2(2x)

    This is the chain rule. In this exercise, the first three derivatives of cos^2(2x) are found. Chain rule is used. A free example (1+3x)^8 involving chain rule is also included.

  • Chain rule

    This provides an example of using chain rule to find derivatives.

  • Differentiation

    14740 Derivatives using product rule, quotient rule, or chain rule. Find the derivative of each expression, using the product rule, quotient rule, or chain rule. 1. P= e^(2x)/x 2. B= square root of sin * square root of x 3.

  • Partial derivatives

    Find the indicated partial derivatives. 1.) f(x,y)= sin(y-x); df/dx(3,3) Using the chain rule, Therefore, at (x, y) =(3, 3), 2.)z= (x^3 + y^3)/(x^2 + y^2); dz/dx, dz/dy Using chain rule and quotient rule, Similar to x, we find the

  • Apply the chain rule to finding partial derivatives.

    The chain rule to is applied to finding partial derivatives.

  • Finding derivatives using the Chain rule

    The expert finds the derivatives using the chain rule function.

  • Using the Chain rule for derivatives in higher dimension

    204667 Using the Chain rule for derivatives in higher dimension Let f(u,v,w) = (eu-w, cos(v+u)+sin(u+v+w)) and g(x,y) = (ex, cos(y-x), e-y). Calculate f o g and D(f o g)(0,0). The solution is attached.

  • Chain Rule : Finding Where f is Differentiable

    109533 Chain Rule : Finding Where f is Differentiable Using the chain rule, show that if z = y + f(x^2 - y2), where f is differentiable, then partial derivatives y(dz/dx) + x(dz/dy) = x Please see the attached file for the complete solution.

  • Partial Derivatives using Chain Rule

    309865 Partial Derivatives using Chain Rule Need help finding partial derivatives of attached problems.

View More Related Solutions