An object is dropped off a building. Ignoring air resistance, the height above the ground t seconds after being dropped is given by h(t) = −16t2 + 140 feet. (a) Use the limit definition of the derivative to find a rate-of-change equation for the height. h'(t) =       feet per second (b) Use the answer to part (a) to determine how rapidly the object is falling after 1 second. feet per second

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the equation of the tangent line to the graph of y at (2, 금). Use the limit process in finding…

A:

Q: By using the definition of the derivative, find the for: - dx 1- f(x) = Vx

A:

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

A:

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: use the definition of derivative to find the equation of the tangent line to the graph of f(x) = x2…

A: To find the equation of tangent line at the given point.

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Topic:- calculus

Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Find the derivative of the function f(x,y) = x +xy + y at the point (- 2,- 1) in the direction in…

A:

Q: Find the derivative of the function f(x.y) = tan -1y at the point (- 9,9) in the direction in which…

A: To find the derivative of a function at a point (-9, 9) in the direction in which the function…

Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

A:

Q: (x-y) atfy (1, 1) a+y

A:

Q: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 5s

A:

Q: Let y = 6Vx. (a) Find using the derivative definition. (b) How fast is y changing when x = 9? %3D…

A: Use the defination of derivative and find the dy/dx dy/dx at point x = 9 gives the slope of tangent…

Q: Find the derivative of the function without using the Quotient Rule. y

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x? +…

A: We need to find instantaneous rate of change of  f(x)=2x2+5x+7 at x=3, using limit definition of the…

Q: Find the derivative of f(x)=arctan(1/x) and simplify

A:

Q: Use three-point midpoint formula to evaluate the first derivative of y=tan(x) at x = O-2√/2 00…

A: Given function is y=tanx. We have to evaluate the first derivative of y=tanx at x=π4 using a value…

Q: What is the derivative of * y = arctan(x2 + 1)?

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x)=6x2+2x+3…

A: The limit definition of derivative is given by: We know that f(x) = 6x^2 + 2x + 3  Now we will find…

Q: Find the derivative of the function without using the Quotient Rule. y =

A:

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

A:

Q: 3/x +1 f(x) = X+2 at x = -1

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 3x + 5x…

A:

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: The size of a population of butterflies is given by the function. p(t)= 6000/(1+49(0.6)t) where t…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = (x2 + 1) sech (ln x)

A: Given: y=x2+1sechlnx

Q: Find the derivative of the function. y = tan−1 (square root of x - 4)

A: Consider the given function. y=tan-1x-4 The objective of the problem is to find the derivative of…

Q: (a) h(x) = tan(r'sinx

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x +5x…

A:

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: What is the derivative of y = arctan(x² +1)?

A: Find the derivative of the function

Q: Find the derivative of the function.

A:

Q: Calculate the derivative of f1 (x) = √1−2x by using the definition of the derivative as the limit of…

A:

Q: What is the Derivative of: y = extan x

A: Given: y=ex tan x To Find: dydx=?

Q: Find the equation of the line tangent to the graph of the function f(x)=x-2x^2 at x=1 use the…

A: The equation of the curve is: f(x)=x-2x2

Q: Let f(x) : 3x Using the limit definition of the derivative, find the equation x +1 of the line…

A: Given data: The given function is f(x)=3x/(x+1). The given point is (a, b)=(2, 2). The expression…

Q: Find derivatives of f(x) = {x+- 1 and find the line tangent to it when x = 1

A:

Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: Find the derivative of the function without using the Quotient Rule. y = -

A:

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: the derivative of f(x) = xi at the point x = 4?

A:

Q: What is the derivative of y = etan-1 2x 2

A:

Q: Find the derivative using the definition 1- y = vx -1

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 7x² + 2x…

A:

Q: How do you find the derivative of the quotient of two functions that are differentiable at a point?

A:

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: