The approximate rate of change in height of a certain shrub in a nursery is given by f ' ( x ) = 13 / x  where the height is measured in inches and x represents the number of years since the shrub was planted. After 2 years, the shrub was 18 inches tall. Find the function that gives the height of the shrub x years after it was planted. Assuming that the shrub will be sold when it is 5 years old, approximate its height when it is sold.

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

A:

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

A: We will use the power rule:

Q: 1+ln(3x²) y = 1+ln(4x) ||

A: Given function - y = 1+ln3x21+ln4xDifferentiating on both sides with respect to x - dydx =…

Q: Find the second derivative of the function f(x) = 3*(square root of x+2 divided by 2x +1

A:

Q: Find the 3rd derivative of the function y=ex/x.

A:

Q: Find the derivative of the function f(x) = x√ln x

A: Here given Use the formula of product rule of derivatives as

Q: Find the instantaneous rate of change in f(x)= 3/x^2 at x=-2.

A:

Q: find the derivative using logarithm of y= (x+2)^2

A: Take ln on both sides Then differentiate both sides with respect to x

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

A:

Q: The approximate rate of change in height of a certain shrub in a nursery is given by f ' ( x ) = 12…

A: f'x=12x Integrating with respect to x on both sides, we get ∫f'x dx=∫12xdx⇒fx=12·lnx+C   →1…

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+1

A: By using the formula you can solve the given problem as follows :

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: y у %3 4a/сosh a

A: Consider the given hyperbolic function y=4acosha The given function can be written as, y=4acosha=4a…

Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: (x) = ,2x+1

A: Explanation and solutions is given below....

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: How do you find the derivative of the sum of two functionsƒ + g?

A: we have to determine how to determine the derivative of the sum of two functions that is f+g.

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: 1 Find the function whose derivative is (x+1)-

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x)=x2+4x at x=-4

A: The instantaneous rate of change of a function at a point can be evaluated first by finding the…

Q: Find where the first derivative is equal to 0. Er ****. lif

A: Introduction: The concept of critical point is very important in Calculus as it is used widely in…

Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

A:

Q: Find the derivative of the function f(x) = 1+ ex

A: First I have written the formula of quotient rule of derivative, just use the rule for given…

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

A:

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: x(2x+3) 17. f(x) =- (x° +1)

A:

Q: when you have f(x) = x^2 + 7x +10 / x^2 - 7x +6 what is the average rate of change of the function…

A:

Q: Find the 4th derivative of x^10 evaluated at x=0. What would be the 100th derivative of x^2000 be at…

A:

Q: What is the difference of antidifferentiation and anti-derivative?

A:

Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

Q: find the 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

A:

Q: What is the derivative of: log x/(x+1)

A:

Q: Find the derivative. y =(ln(ln x))3

A:

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

A:

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

A:

Q: Find the derivative of the function g(x) = ln ex/(1 + ex)

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: Find the 2nd derivative of the given function fCt) = t² Int

A:

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: Find the derivative of the function. g(x) = 2(3- Ex)

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 3rd derivative of the function y=exx.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get

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 the logarithmic functions: y = ln ( 4x^3 - x^2 + 1^2)

A: Application of derivatives

Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

Q: Find the derivative of the function. h(x) = log4(x + 9) h'(x) =

A: Topic = Derivative

Q: Solve the derivative of f(x)=−1/√5 x.

A: we have to find the derivative. f(x)=-15x