gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t). According to the model, how fast were per capita sales of bottled water changing in 2011?

Q: y = (x+1)arccsc(x²) .2'

A: Given: y=x+1csc-1x2 Product rule of differentiation states, ddxuv=v·ddxu+u·ddxv Differentiating the…

Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Find derivative of y=2e^.6t

A:

Q: give the derivative of y = x^6

A: Solution-

Q: What role does the derivative play in defining slopes, tangent lines, and rates of change?

A: To determine the role of derivative of a function in defining slopes, tangent lines and rate of…

Q: In physics, the kinetic energy, K, of an object of mass m, moving at a velocity v, is given by the…

A: Given that kinetic energy K for an object of mass m and velocity V is given by K=(1/2)mv2. If mass…

Q: What information about a graph can be found from the second derivative?

A: What information about a graph can be found from the second derivative?

Q: what is the derivative to y= e^-1?

A: Given,

Q: Find the derivative of the given function.     y=x^(11/5)

A: (d/dx)(x^n)=nx^(n-1)

Q: Evaluate the derivative of y=(cosh'(4x))* . Give your answer in natural logarithmic form.

A:

Q: What is the fourth derivative? x^12+1

A:

Q: Construct an equation where the derivative of said equation is 1. Please involve quotient rule in…

A: To construct an equation where the derivative of said equation is 1. To involve the quotient rule in…

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: 3. As light passes through water, it is gradually absorbed. The percent of light absorbed, 4, as a…

A:

Q: What is the derivative of ( 6 t cott−4e^t)

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: