Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation P = 95e−0.491t. (a) Use the derivative to find the rate at which the pressure is changing at any time t. P'(t) =     (b) Use the derivative to find the rate at which the pressure is changing after 0.6 second. (Round your answer to one decimal place.)   ----   (c) Is the pressure increasing or decreasing? The pressure is increasing. The pressure is decreasing.

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function y = sech(4x − 1)

A: We use the chain rule to find the derivative.

Q: Calculate the derivative at the point (0,0) of the function given by the equation x5+y5−2x+2y=0.

A:

Q: Use the definition of a derivative to find the equation of the tangent line at the given point.…

A: The equation of the tangent line is  y-7x+2=0

Q: What is the meaning of a derivative?

A:

Q: Discuss how the concept of instantaneous velocity v(t) can lead to the mathematical notion of a…

A: Topic:- application of derivatives

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

A:

Q: What is the derivative of y = (inverse tangent(3x))^2 ?

A: We will differentiate the given function with respect to X and use chain rule while differentiating.

Q: In(x²) What is the derivative of

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 second derivative of y=(tan(2πx))^3.

A: giveny=(tan2πx)3 diffrentiate by chain ruley'=3(tan2πx)3-1sec22πx.(2π)y'=6π(tan2πx)2sec22πx

Q: Find the derivative, if y = (log x)" +(sin x)™* -x %3D

A:

Q: Find the derivative of y=sinh-17x

A: Given:y=sinh-17xHyperbolic Identity:cosh2x-sinh2x=1Differntiation formula:ddxsinx=cosx

Q: 40 60 100 What is the derivative of y(t)?

A:

Q: Find the derivative of: y? – 4x = 0 at point (4,4)

A:

Q: cosx y =-

A:

Q: Find the derivative of the function. f (x) = 1/ ( 1+ sec x ) 2

A: Consider the given function, fx=11+secx2 it can be also written as, fx=1+secx-2 now differentiate…

Q: Find the derivative of the function. y = 3 tan-(x - V1+ x?

A:

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: Find the derivative of the function. Vs - 4 f(s) = Vs +2 f'(s) =

A:

Q: What is the first derivative of s(æ) = 4e"*.

A:

Q: What is the derivative of y = e3 In(5 + e3)? %3D

A:

Q: With respect to x, what is the derivative of: * H5 du -3/5 Option4 Option 2 2/5 du -3/s du dx…

A:

Q: at x: つ:8ー5x, atx=e

A: Given:  F(x) = x3 - 5x ...(1)       and the…

Q: The derivative of ye* + xe + x + y=0

A:

Q: Find the derivative of the function. Vs - 1 f(s) = Vs +5 l'(s)=]

A: Given query is to find the derivative of the function.

Q: FIND THE DERIVATIVE OF THE FUNCTIONy=0.6e to the fifth(x) degree

A: The given function "y" is shown on the white board. We need to find its derivative. Before we get…

Q: Why is the notation dy/dx used to represent the derivative?

A:

Q: Find the second derivative of the function. f(x) = sec x * "(x) = Noc

A: Please see the explanation below

Q: Find the derivative of the function.

A:

Q: What is the derivative of (x^2+1)^x?

A: Use the lograthim to find the derivative of given expression.

Q: What is the second derivative of y = sec “(3 x) ?

A: For the question 1, none of the options match. If the question had asked for first derivative of y…

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: f y = (sin x)x b

A:

Q: What is the Derivative of yx

A: f(x) = yx

Q: Find the derivative of y with respect to x for y=2x   ???

A: y=2x

Q: Find the derivative of y= log, (5x³)+log, (sin.x)

A:

Q: 1. What is the derivative of f(x) = x2 – 8x + 12 when you illustrate using tangent? 2. What is the…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Find the second derivative of the equation below evaluated at y = 1:

A: Given that: The implicit equation 4 e y + x y = 4e.

Q: What is the derivative of cy = 2 - a°y ?

A:

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

A:

Q: Which of the following is not an equivalent way of expressing the term "derivative?"

A:

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: If y=x+ 4÷x+1 use the first derivative test to find where relative extrema occur.

A:

Q: Can you help me find the fourth derivative of y=1/√x?

A: We have to find

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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: