Find the solution of each of the following initial-value problems.
Step 1 of 3
Chain Rule We need to find derivatives of compositions of 2 or more functions. Ex. f(x) = sin(x^2), g(x)= x + 1, h(x)= cos(sintan(x)) The chain rule F(x)=f(g(x)), F’(x)=f’(g(x))*g’(x) Ex. F(x) = sin(x^2) the other function f(g(x)) is sin(g(x)) the inner function g(x) is x^2 F’(x) = cos(x^2)*d/dx x^2,cos(x^2)*2x Ex. g(x) = x + 1, d/dx( x + 1) = d/dx (x^2+1)^½ The outer function is the power of ½, the inner function is x^2 +1 d/dx [ x^2 +1)^½] = ½(x^2+1)^-½* d/dx(x^2+1) = ½(X^2+1)^-½*2x this answer is perfectly acceptable Ex. d/dx [(x^4+x)^10] = 10(x^4+x)^9 * 4x^3 +1 Ex. d/dx (sin^8(x)) Remember sin^n(x) = (sin(x))^n So d/dx [(sin(x))^8] =8(sin(x))^7 * cos(x) Mini Formula = d/dx ((f(x)^n) = n/f(x))^n-1 * f’(x) Advice always rewrite trig functions like the equation above
Textbook: Differential Equations and Their Applications: An Introduction to Applied Mathematics
Author: M. Braun
This full solution covers the following key subjects: . This expansive textbook survival guide covers 65 chapters, and 855 solutions. Since the solution to 9 from 2.1 1 chapter was answered, more than 207 students have viewed the full step-by-step answer. Differential Equations and Their Applications: An Introduction to Applied Mathematics was written by and is associated to the ISBN: 9780387908069. This textbook survival guide was created for the textbook: Differential Equations and Their Applications: An Introduction to Applied Mathematics, edition: 3. The full step-by-step solution to problem: 9 from chapter: 2.1 1 was answered by , our top Math solution expert on 03/13/18, 07:00PM. The answer to “Find the solution of each of the following initial-value problems.” is broken down into a number of easy to follow steps, and 10 words.