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)
Using Cramer's Rule with a 3x3 system 3x+4y+z=17 2x+3y+2z=15 x+y =4
Given the function f(x) = e^(2x) a) Find the derivative b) Find the inverse (i.e. g(x)) c) Find the derivative of the inverse d) Find the value of g'(pi)
Find a real valued function such that its derivative exists in every point, but it is not continuous at least in one point.
The process of working with the definition of the derivative is shown using the example f(x)=3x-6.
The idea of the derivative is explained using the function x^2.
Use the (limit) definition of the derivative to find the derivative of f(x)=3x^2-2x+1?
Let f(x) be a continuous function of one variable. a) Give the definition of the derivative. b) Use this definition to find the derivative of f(x)=x^2+2x-5 c) Evaluate f'(2)
Context: We are learning Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class. We just finished continuity and are now studying differentiation. Question: Let f: [a,b] --> R, a < b, twice differentiable with the second derivative continuous such that f(a)=f(b)=0. Denote M = sup |f "(x)| where x is in [a,b]
Find the rule for the sequence below. square 2x2 =10 3x3=40 +30=20 difference 4x4=90+50=20 difference 5x5=160+70=20 difference
Find a polynomial p so that: p''(t)+3p'(t) + 2p(t) = (t^2)-2 for all numbers t. (note: p''= p double prime and t^2 = t raised to the power of 2)
Two carts A and B are connected by a rope 39 feet long that passes over pulley P. The point Q is on the floor directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 2 ft/sec. How fast is cart B moving toward Q at the instant cart A is 5 feet from Q? Express solution using related rate n
Find the derivative. a) f= 4-sqrt(x+3) b) f= (x+1)/(2-x) See attachment below for additional information.