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: Find the 5th derivative of the function y=x2sin2x at x=0.

A:

Q: find the derivative of - (z+j)?

A:

Q: find the derivative of tihe unction?

A:

Q: What is the derivative of `y=\ln\ x`?

A:

Q: Find the second order derivative if  y = xx

A:

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

A:

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

A:

Q: The instantaneous velocity of a particle is defined as the derivative of some functions. Select one:…

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: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

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

A:

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Find first the derivative as shown below: f'x=ddx-5-x2        =125-x2ddx5-x2       =-125-x2-2x…

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

A:

Q: Find the derivative with respect to t. y= csc-1(et)

A: Given:

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

A:

Q: calculate the derivative

A:

Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

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

A:

Q: Evaluate the derivative of y =e* sinh (2x). -3x

A:

Q: Find the derivative of the function

A: Given:y=arctanx+x1+x2Differentiate formula:ddxarc tanx=11+x2ddxuv=vdudx-udvdxv2

Q: Find the first derivative y= etanx

A: We have to find first derivative of    y=etanx   First derivative is dydx

Q: what is the first derivative of arccos4x

A:

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

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A:

Q: The second derivative of the function is y = arctan 2x

A:

Q: If y=Incscx, then the value of first derivative (y) is

A: The given function is y=ln cscx.

Q: Find the derivative of the function defined by the equation x+y=arctan(xy).

A: To find the derivative of the given function.

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: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: What is a higher-order derivative?

A: We create, or derive, a new function f'(x) from a function f(x) called as derivative of function…

Q: Find the derivative of y = etanx

A:

Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.

Q: Find the derivative of the secant function y=secx.

A: The give function is y=secx.

Q: Find the most general anti-derivative

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log4 x + log4 x2

A: Given: By using logarithm base change rule, the function can be rewritten as follows,

Q: What is the derivative of y = ekx?

A:

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: find the derivative of y with respect to the givenindependent variable. y = log25 ex - log5 √x

A:

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 value of the derivative of the function y=sinx/3 at x=2π.

A: Here given as Differentiate the above function with respect to x

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

A: y=2x

Q: Which is the first derivative of y=vx ?

A:

Q: Use Delta method to find the derivative of e*

A:

Q: Find the derivative of g(x) = fecost dt.

A:

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: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

Q: find the derivative of y with respect to the givenindependent variable. y = log3 (1 + θ ln 3)

A:

Q: Which is the first derivative of y=vx ? *

A: Given Data: y=x Formula: d(xn)dx=nxn-1

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: