Find an expression for the derivative of the exponential function y=ex using the definition of derivative.

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

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

Q: 3.) y = log2 – 6·x³

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

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

A:

Q: Use logarithmic differentiation to find the derivative of the function. y = (3x + 2)4(4x − 3)2

A:

Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 2n +4n in (2n) X

A: Follow the procedure given below.

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

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: Evaluate the derivative: y = log2(log2x)

A: It is given that,

Q: Find the derivative of function. y = log2(2x2 - x)5/2

A: Given, y = log2(2x2 - x)5/2 To Find the derivative of function.

Q: Use logarithmic differentiation to find the derivative of the function. y = xln(x)

A: aur objective is to find the derivative.

Q: x+1

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

Q: Use logarithmic differentiation to find the derivative of the function. y = x4/x y'(x) =

A:

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

A:

Q: Find the derivative of f( x ) = log3(x + 6.5). f'(x) =

A:

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

A:

Q: Solve for the second derivative of the following implicit function

A: We can solve this as follows:

Q: Use logarithmic differentiation to find the derivative of the function    y=(2x+1)5(x4-3)3

A: Given,          y=2x+15x4-33

Q: find the derivative of: f(x)= x^(1/x) using logarithmic derivatives

A: Given function

Q: Find the first derivative of the function below:

A:

Q: Find the derivative of f(x) = log3 5x2 +1

A: Find the derivative of fx=log35x2+1

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: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

Q: use logarithmic differentiation to find the derivative of y=(x^2+3)(x-1)^2(x-2)^1/3

A: Applying natural logarithm on both sides, we get

Q: Use logarithmic differentiation to find the derivative of y. 22) y = /x(x+ 5)

A:

Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: х — 3 y = х° + 3

A: topic - logarithmic differentiation

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+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: Use logarithmic differentiation to find the derivative of the equation. Y= (x + 1)^2*(x + 2)^3

A:

Q: Find the derivative of the function y = log3(x2 − 3x)

A: Consider the following: y=log3x2−3xDifferentiate w.r.t.…

Q: The 4th derivative of the given function is ソ= 2e2x

A:

Q: Find the derivative using logarithmic differentiation. x(x+4) (5x + 1)(3x +7) y =

A:

Q: Use logarithmic differentiation to find the derivative of y. 20) y = (x4 + 1)³(x - 1)2x4

A:

Q: f(x) = log,(x² – x + 3)

A: Given: f(x)=log4(x2−x+3)

Q: Explain briefly how we can compute the derivative of a function y=f(x) using logarithmic…

A: Logarithmic differentiation is an important method of differentiation. To find the derivative of the…

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

A:

Q: Use logarithmic differentiation or an alternativemethod to find the derivative of the function  y =…

A: the given function is: y=xx we have to use the logarithmic differentiation or an alternative method…

Q: Find the derivative of the logarithmic function. y = In Isec x + tan x|

A: We have to find the derivative

Q: Find the derivative of the natural logarithm y=lnx.

A:

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

A:

Q: What is the derivative of e^-x

A: Given query is to find derivative of e-x

Q: XV X-+9

A:

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

A: Given function, y=x4x

Q: Find the first derivative of the following functions

A:

Q: 2x+3) 17. f(x) =- (x² +1)*

A: topic - logarithmic differentiation

Q: Find the derivatives of x log x.log(logx)

A: We have to find the derivative of-  x logx.log(logx)

Q: what is the Derivative of Exponential Functions?

A:

Q: Use logarithmic differentiation to find the derivative of the function. y = (x3 + 2)2(x4 + 4)4

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: