Suppose that the growth rate of a duckweed plant in a standard growth medium is given by W (t)=0.15e025t , where t is measured in days and W (t) is measured in day grams (a) Find a formula for the weight of a duckweed plant, W(t), assuming that W(4)=2.13 grams. Check your answer in using differentiation

Q: Find the derivative of the function = etan(e) y' =

A: y = etanθdydθ = detanθd(tanθ) × d(tanθ)dθdydθ = etanθ.sec2θ

Q: 3. Use logarithmic differentiation to find the derivative of y with respect to the given independent…

A: we have to find the derivative of y by using logarithm.

Q: If y = xtan (a), find y' by using logarithmic differentiation.

A: Important logarithmic property: ln(xn) = n*ln(x)

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: Give the derivative formula for the function. j(x) 4 In x e5 = j(x)

A: The function is given by,

Q: Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is…

A: To show that the given function ft=sinet2 is of exponential order.

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

A:

Q: Find the derivative of k(x) = log3(x) cos

A:

Q: 2х- 3 3. У3 5x +1

A:

Q: y = In- e 2x+1

A:

Q: Find the derivative of the function.

A:

Q: Find the derivative of the logarithmic function. 6 + y = In

A:

Q: Find the derivative of the function f(x) = ln(e" + 5).

A: We have to find the derivative of the function -          f(x)=ln(ex+5) Here , we will use the…

Q: Find the first derivative of the following functions with respect to x y = In(ln(In x))

A: To find first derivative of the given function.

Q: Find the second derivative of the following function at x = 2 y = (x +) 2 G+x)

A: Given function is y=x+1x2

Q: Find the derivative of the functions below: In(x) (a) g(x) = log,(x) g'(x) = (b). y- in(6x®)

A:

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: Find the derivative of y with respect to the independent variable. x8)n 5) y =log 5 x-8

A: using the fact of logarithmic  logax=lnxln(a) find the derivative

Q: )=1/x. Using this, compute the

A:

Q: Verify that the derivative and integral results for a general base b reduce to the expected results…

A: Note that ddxbux=lnbeuxu'x,∫bxdx=bxlnb+C.

Q: Determine whether the following statement is true or false, and explain why. The derivative of ln kx…

A: if y = ln x Then y'=1x

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: What is the derivative of log a x? Are there any restrictions on a?

A: Given function is,

Q: Find the derivative of the function. y = e In(7x)

A:

Q: Find the derivative of y with respect to x. y=log(base)5 e^7x

A:

Q: 5. y³ = 4(y + x²)

A:

Q: Calculate the derivative of the function y = (6^6 + 3)^x using the fact that b^x = e^(x ln b) and by…

A: Consider the given function:

Q: Find the derivative of f(x) = In (x* V8 – 6x), using the properties of the logarithm. Provide your…

A: I have stated the used formulas in the solution

Q: 1. Apply the different rules for differentiation in finding the first derivative of the following…

A:

Q: 2. Find the derivative of the function. y = e* In (sinæ)

A:

Q: calculate the derivative of the following function. [ln(x^8)]^3

A:

Q: Find the derivative of the function y, below. y = 6x(ln a + In 5) – 8x + e ||

A: Given that y=6x(lnx+ln5)-8x+e To find the derivative of y

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (θ + 1) - eθ

A:

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: Q3// By using logarithmic differentiation and with respect to independent variable x, find the…

A:

Q: Calculate the derivative of the following function. y=6 log 3 (x - 9) d 6 log 3 (x - 9) =D dx

A: d/dx [ f(x) ] = 1/ f(x) * d/dx[f(x)]

Q: Find the derivative of the function. h(x) = log,(x + 9) h'(x) = %3!

A:

Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: Find the derivative of the function. y = log 6 V3x+7 3. O A. In 6 3 In 6 O B. 3x +7 In 6 (3x + 7) 3…

A: Given, y = log63x + 7Applying the log rule; logab = lnblnay = ln3x + 7ln6Differentiating with…

Q: Find the derivative of the function

A: given h(x)=log3xx-12we have to find the derivative of the given function

Q: Use logarithmic differentiation to find y′, given y = e2x xx √(x3 + sinh(3x))

A:

Q: Solve for the derivative of the following Exponential Differentiation. 1. y = 92x^2 + 3x +1 2. y =…

A:

Q: Give the derivative formula for the function. (x)2 In x -e j'(x)

A: Consider the given function.

Q: Using logarithmic differentiation, Show that y (x)= xa2" e®has no stationary points other than x =…

A:

Q: Find the derivative of the function. h(x) = ln(2x2 + 1)

A:

Q: 2. Use logarithmic differentiation to find y', given y = e2". x* Vx3 + sinh 3x.

A:

Q: Find the derivative of the function. h(x) = log,(x2 + x) h'(x)

A: Differentiation

Q: Use logarithmic differentiation to find the derivative of y with respect to x. y = ( In (3x))n (9×)…

A:

Q: Find an equation of the tangent line to the graph of (log æ)cosh(a-10) , x >1 at the point where x =…

A: Given equation is  y=log xcosh (x-10), x>1 at x=10

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.