Would you be able to find the inverse of this equation y = e^x / 1+6e^x

Q: find y' for y = 2Vsinx sinh-1(logx). %3D

A: y'=log2· 2sinx-1.cosx.sinh-1(logx)sinx+2sinxxlog2x+1

Q: 3.) y = log2 – 6·x³

A: Explanation: Given that,  y=log2(-6x3)

Q: Differentiate y = /sin(x² + 3)cosx

A:

Q: take natural log from both sides and solve the right side using the log rules. Then, take derivative…

A:

Q: The amount of plutonium remaining from 1 kilogram after x years is given by the function…

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: kel derivative

A:

Q: Differentiate  y=sin(ln(5x2-2x))

A:

Q: Without using a graphing calculator, how can I show the function 1-ln(y )= z in a graph and its…

A: Without using a graphing calculator,  Show the function zx,y=1-lny in the graph and its traces.

Q: Differentiate with respect to the independent variable: y=tan[ln(3x2+5)]

A:

Q: What is the derivative of the natural logarithm function ln x? How does the domain of the derivative…

A: Given: fx=ln x To find: (a) The derivative of f(x)  (b) Compare the domain of the derivative with…

Q: Find the first derivative:  y=log1o 5x+3/5x-4

A:

Q: (5) log yz (6) log (7) log (ry) (8) log rvz

A: We will find the value of these problem using logarithm formula.  We know  , log(A/B) = log(A)  -…

Q: Jay and John used to travel together but because of the pandemic, they decided to go separately…

A:

Q: x+1

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

Q: Find the derivative of y =log2x

A:

Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

Q: If 5æ? + 3x + xy = 1 and y(1) = -7, find y'(1) by implicit differentiation. y(1) =

A:

Q: How do you find the derivative of y = ln2x8

A: Explanation of the solution is given below....

Q: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

A:

Q: What are the domain and range of ln x?

A: Given: y=lnx we know that in lnx, x>0 so, domain of given function is x>0

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 What is the family of the equation y %3D quadratic exponential linear

A:

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

Q: Differentiate  y = ln(2x + 1)

A:

Q: The rate of decomposition of radioactive radium is proportional to the amount present at any time.…

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years.…

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

A:

Q: Suppose an unknown radioactive substance produces 800 counts per minute on a Geiger counter at a…

A:

Q: 6. y = (x² – 1)tnx

A:

Q: How the processes of integration and differentiation can be considered as inverses of each other

A: It is known that ∫ fx dx=gx+C, where C is some constant whenever g'x=fx.

Q: Find dx by logarithnic differentiation. (3x-2)(x"+3)

A: d(logx)/dx = 1/x

Q: proportional to A, weight W, and height H. A and W measurement values taken from different people…

A:

Q: A colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

A:

Q: What is the derivative of (ln(3x))/x^6?

A: Let y = (ln(3x))/x6.The derivative of y is with respect to x as follows.

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) 1

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: What is the inverse process of determining a function whose derivative is known?

A: The inverse process of determining a function whose derivative is known is called

Q: Discuss how the processes of integration and differentiation can be considered as “inverses” of each…

A:

Q: Find the derivative of f(x) Give answer in exponential notation with positive exponents

A:

Q: In your own words, explain what a differential is, and what it's used for.

A:

Q: Give one problem and solution for each differentiation rule of exponential functions.

A:

Q: Find the second derivative y" if y = elnx³

A: Given,            y=elnx3

Q: 40. z 10 log y

A:

Q: Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at a…

A:

Q: Give 5 examples of derivative of exponential function with solution

A:

Q: Find the derivatives of 20" log(tan x)

A:

Q: Write the derivative of 7 log8(x)

A: We have to find the derivative of 7 log8(x).

Q: what is the Derivative of Exponential Functions?

A:

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

A:

Q: Find the higher-order derivative. (4 log 2(x – 5)) dx2

A: Given, d2dx24 log2x-5

Q: A certain bacteria culture is observed to double its amount after two hours it was initially…

A: Let say population is P. So population at time 't' is given by P(t). Assume initial population is P0…