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    Derivatives

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    Derivative Functions Written

    Write down the derivative of each of the following functions. f(x)=e^-2x. (thats e to the power minus2x). g(x)=sin(7x). Hence by using the product rule,differtiate k(x)=e^-2xsin(7x)

    Differentiation

    Differentiation of functions. Please see the attached file for the functions.

    Determine derivative

    (See attached file for full problem description) Determine the derivative: 1) d/dx

    Differentiation of composite function - integral form

    (See attached file for full problem description with proper symbols) --- Assume that f is continuous on [a,b], g is differentiable on [c,d], g([c,d]) [a,b] and F(x) = For each x [c,d]. Prove that F'(x)=f(g(x))g'(x) For each x (c,d).

    Divisibility Tests and Rules and Quotient Polynomials

    Let n be a positive integer a) prove that n is divisible by 5 if and only if it ends with 0,5 b) prove than n is divisible by 11 if and only if the alternating sum of its digits is divisible by 11 c) find a similar criterion for divisibility by 7 and prove it .

    Applications of Derivatives Word Problems

    1. Find the point of inflection of the function described by f(x)= x^3- 6x^2+12x- 4. Apply an appropriate test to mate sure it is a point of inflection you found. 2. A large cube of ice is melting so that its volume, V. is decreasing at the rate of 60 cm^3/s. Find the rate at which each side, x, of the cube is decreasing at the

    Revenue, Supply and Demand Functions : Derivatives and Integrals

    5. A man was sentenced to 50 years in prison when he was 20 years old. While in prison he reflected on his life and decided that he should turn his life around and do something good for his society. He then became a model prisoner and his good behavior earned him the privilege to pursue a career in law. When he became 39 years

    Absolute maximum and the absolute minimum, derivatives

    1) Find the absolute maximum and the absolute minimum of F(x)= (x+2)/(x-2) on intervals [- 4,4]. 2) Find the derivative of the following: a- F(x)= e^(2x) x^2 + e^(-x^2) b- F(x)= ln(x^3 - 3)^4 3) Use the logarithmic differentiation to find the derivative of : Y= √(4+3x^2)/(x^2+1)^(1/3) ---

    Implicit differentiation

    Consider this equation: x2 - 2xy + 4y2 = 64 A) write an expression for the slope of the curve at any point (x,y) B) Find the equation of the tangent lines to the curve at the point x = 2 C) find d2y/dx2 at (0,4)

    Differentiation and Derivatives : Chain Rule

    1, f(x) = ln (5x-7) f (g(x)) = ln (g(x)) df / dg = 1 / g(x) g(x) =5x-7 dg /dx = 5 df / dx = df / dg . dg /dx = 1 / g(x) . 5 = 5 / 5x-7 2,using the same philosophy can you show me how to determine the following

    Critical Numbers, Derivatives and Rates of Change

    See the attached file. The function has one critical number. Find it. A student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisone

    Applications of Derivatives Word Problems and Rate of Change

    A street light is at the top of a 14 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole? Note: You should draw a picture of a right triangle with the vertical side representing the pole,

    Differentiation

    Can you please show me how to calculate the following showing full workings? --- 1, Obtain the derivative of f(t) 1n(5-(2/3)t) There are no brackets round 2/3 in the question but my computer skills do not allow me to write it as it should be, hope you understand. 2, Determine f ′ (t) if f(t) = G(1 -

    Stochastic Differential Equations

    Prove by differentiation that if D is a constant, the function f(x,t) = 1/(sqrt(2*pi*D*t)) * e^ ((-x^2)/(2Dt)) is a solution of the differential equation (delta f)/(delta t) = D/2 * (delta^2 f)/(delta x^2)

    Interest and applications of derivatives.

    A person's fortune increases at a rate to the square of they're present wealth. If the person had one million dollars a year ago and has two million today then how much will the person be worth in six months?

    Implicit Differentiation Investigation

    Use implicit differentiation to find the slope of the tangent line to the curve at the point . Find by implicit differentiation. Match the expressions defining implicitly with the letters labeling the expressions for . 1. 2. 3. 4. A. B. C. D. Let Let Let Then