g(x) = x'n(x) %3D

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

A: Use derivative formula :- f(x) = lnx then derivative f'(x) =1/x

Q: The derivative of y = 2 ln ⁡ x − ln ⁡ x 3 is

A: The given function is, y=2lnx-lnx3

Q: Find the first derivative of y = (ln x)4

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

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: Find the 3rd derivative of the function y=excosx.

A:

Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: find the derivative of the function  y'=ln(squared root of x^2-4) and  y=ln IsinxI

A: The given function is y=lnx2-4. Obtain the derivative as follows.…

Q: Find the derivative of y=ln[x^3(x^2-5)^3/4]

A:

Q: Determine the derivative of f(x)=ln(x√x^2+1).

A:

Q: Find the derivative of the function y = ln(9 – e-ª).

A:

Q: Find the derivative of the function.

A: Given y=lnx+1x-1

Q: find implicit derivative of x^3 + x tan^-1 y = e^y

A:

Q: Find the derivative of the function. y = ln√(x2 − 4)

A:

Q: Find the second implicit derivative of the given using implicit differention y2-3x+2y=0

A:

Q: Compute the derivative of the function y=x2/ln x at x=e.

A:

Q: Find the derivative of the function y = ln(9 – e-"). f'(x) =

A: Given that y=ln(9-e-x) To find : Differentiation  y'=f'(x)=ddx(ln(9-e-x))=19-e-xddx(9-e-x)=e-x9-e-x

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: find the first and second derivatives of f(x) = ln (x+1)

A: f'(x)=1x+1 and  f''(x)=-1(x+1)2

Q: find the derivative for  h(x) = 3e ^ -x * ln(2x+1)

A: Using product rule of derivative In order to solve the given problem.

Q: Find the derivative of y= ln (6X^2+3X)^3/(7X-2)

A: Topic-Derivative

Q: Find the second derivative of g(x) = sinh(x) cosh(x)

A:

Q: Find the derivative of z=(ln5)e^x dz/dx=

A:

Q: Find the first derivative of = (ln x)* 4 y

A: From the given function; y=lnx4 We know that; The Power law: ddxxn=nxn-1 The chain rule:…

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: y ln x − x ln y = 1

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: What is the first derivative of the expression (xy)× = e?

A: See the details solution in below

Q: Find the derivative of the function. y = ln∣csc x∣

A: Given data:   The given expression of the given function is: .   Substitute u for csc x in the given…

Q: Find the derivative of the function. y= log 4- x

A:

Q: Find the derivative of the function. y = tan−1 (square root of x - 4)

A: Consider the given function. y=tan-1x-4 The objective of the problem is to find the derivative of…

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(x − 1)

A:

Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: Find the derivative of the function: f(x)=ln[x^2÷(x+1)^3

A: Formula:

Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

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

A:

Q: Find the derivative of -3x f(x) = e¯* + e2x - e %3D

A:

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A:

Q: find the first derivative in the form of dy/dx y=(3x-ln(x))^5

A:

Q: Find the first derivative of y = cos*x- sin*x.

A:

Q: Find the 3rd derivative of the function y=exx.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get

Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

A:

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

A: Application of derivatives

Q: Find the first derivative of h(x) if h(x) = cos (x – 2x) -

A: h(x) = cos2(x3-2x)

Q: Find the second derivative of y=x-1 at x=2

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log3 (1 + θ ln 3)

A:

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

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

A:

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

A:

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: