calculate the value of k, when the inverse function of y = 3 ^ x is y = k × ln (x).

Q: Compute the derivative.    f'(3),   f(x) = log5 x

A: Given: fx=log5 x  ……1   To find: f'3

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

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

Q: Differentiate y = /sin(x² + 3)cosx

A:

Q: Find y' for y = (2(x^2+1))/(x(sqrtx+1)) using logarithmic differentiation

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

A:

Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

Q: State the derivative. Do not simplify. f(x) = log(x) + log₂ (x)

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: 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: x+1

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

Q: Find using logarithmic differentiation if y = (2z). dr %3D

A:

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

A:

Q: Find the derivative of the function g(x) = log3 √(1 − x)

A:

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

A:

Q: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

Q: 4. Use logarithmic differentiation to find the derivative of the function y = x c0sx.

A: So we are going to take natural logrithm to both side and solve them so I'm providing hand written…

Q: Differentiate the following function.   y = ln(3x+1) - ln 3

A: We need to differentiate the following function.   y = ln(3x+1) - ln 3

Q: Evaluate the derivative. * d (log10 (x)) dx (In(10)) O Option 1

A: we have to find the derivative

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 first derivative of q(x)=(3x)7x at x=2?  Enter an exact answer in terms of a natural…

A: When there is variables in exponent we should take log both side then differentiate. Here we use…

Q: 2. y=cot1-2x 3. y=log22x*

A:

Q: Calculate the derivative and use logarithm rules to simplify   g(x) = ln((x^3 + 2x)(x+1)^10)

A:

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

A:

Q: Use properties of logarithms to find the derivative of f(r) = In ((2. 2)

A:

Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

Q: x(2x+3) 17. f(x) =- (x° +1)

A:

Q: 6. y = (x² – 1)tnx

A:

Q: Find the derivatives of function (log x)tanx

A:

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

A:

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: Find the nth order derivative of the natural logarithm function y=lnx.

A:

Q: Find the second derivative of 2x^2 ln (1/x^2)

A:

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: 4. y=ln(4x' +5)

A:

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

A:

Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

Q: 3 sin-xe 5%

A:

Q: 2. Use the logarithmic differentiation to simplify completely before finding the derivative.…

A: As per our company guidelines we are supposed to answer ?️only first question. Kindly repost other…

Q: 2x+3) 17. f(x) =- (x² +1)*

A: topic - logarithmic differentiation

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

A: Application of derivatives

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

A:

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

A:

Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

A:

Q: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10

Q: what is the Derivative of Exponential Functions?

A:

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

A: Topic = Derivative

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: