A lighthouse is 30 miles off a straight coast and a town is located 25 miles down the sea coast. Supplies are to be moved from the town to the lighthouse on a regular basis and at a minimum time. If the supplies can be moved at a rate of 4 miles per hour on water and 40 miles per hour on land, how far from the town should the do
Find the derivative dy/dx if y = x^(x+3)
The heat transfer in a semi-infinite rod can be described by the following PARTIAL differential equation: ∂u/∂t = (c^2)∂^2u/∂x^2 where t is the time, x distance from the beginning of the rod and c is the material constant. Function u(t,x) represents the temperature at the given time t and p
Find the derivative of the function y=x^2e^(3x) See Attachment for a cleaner version of the question.
Let f be a function given by x + 2 if x < 0 f(x) = x if x >= 0 Is there a function g: R ---> R such that g'=f? *be careful applying definition of the derivative
I want to prove, for the numbers a and b, that the following equation has exactly three solutions if and only if 4a^3 + 27b^2 < 0: x^3 + ax + b = 0, x in R
At what rate is the surface area of a cube changing the edge measures 5 inches and is changing at a rate of 2 in/min. GIVEN (A=6*s^2)
Prove that if f(x) = x^alpha, where alpha = 1/n for some n in N (the natural numbers), then y = f(x) is differentiable and f'(x) = alpha x^(alpha - 1). Progress I have made so far: I have managed to prove, (x^n)' = n x^(n - 1) for n in N and x in R both from the definition of differentiation involving the limit and the binomial
Find partial deriv's w/r and w/theta using appropriate chain rule for : w=the square root of (25-5x^2-5y^2), where x=r cos theta, y= r sin theta.
A) z=y^3-4xy^2-1 B) first partial derivative WRT x,y,z for : w=3xz/(x+y)
Given The Maclaurin series for the inverse hyperbolic tangent is of the form x+x^3/3+x^5/5...x^7/7. Show that this is true through the third derivative term.
Use the product rule find derivative of h(t)= cubed root of t * (t^2+4)
Find the first partial derivative with respect to x, y, z. w = 3xz / x+y
Let f be the function: F(x) 1/4 x=o, x 0<x<1 3/4 x=1 Using standard partition Pn (0,1) where n greater or equal to 4 L(f, Pn) = 2n(squared) -3n+4 all divided by 4n(squared) U(f,Pn) = 2n(squared) +3n+4 all divided by 4n(squared) and deduce that f is intergrable on (0,1) and evaluate (intergral sign with 1 at t
1.) Find the derivative of the function: a.) f(x) = x + 1/x^2 b.) f(x) = (2/3rd root of x) + 3 cos x 2.) Find equation of tangent line to the graph of f at the indicated point: a.) y = (x^2 + 2x)(x + 1) ; (1,6)
The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t) To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t. a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of
What is the equation of the reversal tangent of the following function: f(x)=-(x^3)+9x^2-(29x)+35
What is the equation of the reversal tangent of the following function? f(x)=-(x^3)+9x^2-(29x)+35
Use implicit differentiation to find dy/dx if y^2 + 3xy + x^2 + 10 = 0 (1) where y is a function of the independent variable x.
Using the definition of the derivative and any standard limiting theorems, show that the derivative of (sinx)^2 is sin(2x).
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)
For the curve f(x) = x - 1/3x^2 (one third x squared), find the equation of the straight line which is tangent to this curve at the point x = 1. See attachment for diagram.
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)
Find the first and second derivatives of the function y=((1-x)/x^2)^3