differentiate the function: f(x) = 6x ln(5x) -6x f'(x)=

Q: Find the derivative of the function.   f(x) = x5 ln(x)   f'(x)=

A: We have to find the derivative of function: fx=x5lnx Here there are two function in multiplication…

Q: 11. y=3x+ ln x %3D

A: Topic - derivatives

Q: Differentiate the following function.   y = ln(x2 + ex)

A: Given function is y=lnx2+ex. To differentiate the function. Solution: Power rule of differentiation…

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 derivative using the logarithmic y=ln (x+1)/x^2-2

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: find nth derivative of y=x/(x+1)^4

A: To find the nth derivative of the function y=x(x+1)4=x+1-1(x+1)4=1(x+1)3-1(x+1)4

Q: compute the derivative f (x) = ln(4x2 + 1)

A:

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

A:

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: Compute the derivative in terms of log for y=log(xe^(-3x))

A:

Q: Use the logarithmic differentiation to find the derivative of the function. y= (sin(2x))^ln(x)

A: Topic- Differentiation

Q: f (x) = ln(x · 5*)

A:

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: Find the derivative. y = (ln x)2

A:

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

A:

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

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

A:

Q: Differentiate the function   f(x) =    1/  ln x

A: Given function is fx=1lnx We know that 1an=a-n So, given function can be written as fx=lnx-1 Before…

Q: Use logarithmic differentiation to find the derivative of y. 24) y = Vx(x + 3) %3D

A:

Q: Find dy/dx by implicit differentiation. x4 + yA 5

A:

Q: Find the derivative of the function. y = x2 ln x2

A: Consider the provided question, We have to find the derivative of the given function,

Q: Find the derivative of the function y = ln 4x / (x − 6)

A:

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

A:

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

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: Find the derivative of the function. f(x) = x6 ln(x)

A:

Q: Find the second derivative of the function. g(x) = √x + ex ln x

A: Consider the given function gx=x+ex lnx Now, differentiate the given function with respect to x…

Q: Find the derivative of the function. f(x) = ln(4x)   f '(x) =

A: Given function

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

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: Differentiate the function. y=ln(x5sin2x)

A: Given function:

Q: Find the 1400th derivative of f(x) = xe-X.

A: Here we find derivatives of function.

Q: 4x dx

A:

Q: Find the derivative of y= log, (5x³)+log, (sin.x)

A:

Q: Find the derivative of f(x) = ln v4 – x2 %3D

A:

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

A:

Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

A:

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: Find the derivative using logarithmic differentiation  y= x(x2+1)/sqr root x+1

A:

Q: Find the first derivative of:   f(x) = ln [(5x+2)1/2 / csc(x)]

A:

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: Use logarithmic differentiation for find for y = (x-12)² dx x-8

A:

Q: Find the derivative of f(x)= ln x^2/x^2+1

A:

Q: 3. Use logarithmic differentiation to find the derivative of the function. (2x – 1) Vx+1 y =

A: giveny=(2x2-1)5x+13taking log on both sidelogy=log(2x2-1)5x+13using log…

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

A:

Q: Find the derivative.  y = ln((x + 1)(2x + 9))

A:

Q: Find the derivative of f(x) = 3/x ln(x), f' (æ) =

A: Chufu

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: