Find f'(5) for f(x) = ln(3x +e-0.04=). Round the result to 4 decimal places. f'(5)

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

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

A: Topic - derivatives

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: 14. If x2 + y2 13, find at (2, 3). dx2 %3D

A:

Q: 3.

A: Indefinite Integration

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: 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: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

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Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

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: 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: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

A:

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: 11) Find the first derivative of y = (lnx) 4

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

A: Topic-Derivative

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 derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

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

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Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

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

A: See the details solution in below

Q: Find the derivative. y = 7x ln(6x) dy dx

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Q: Find the derivative y=ln(2x^3+6x-1)^3

A: y=ln2x3+6x-13 take derivative y'=ddxln2x3+6x-13 y'=12x3+6x-13ddx2x3+6x-13

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: Find the second derivative if y = sinh- (n + x') at x = 0

A:

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

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 equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

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

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Q: Find the derivative of the function g(x) = ln ex/(1 + ex)

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Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

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

A:

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

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

A: Apply exponent rule:

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

A:

Q: Find the nth derivative of the function y=xlnx at x=1.

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

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

Q: What is the derivative of the function  x^8(ln(x))?

A: To find the derivative of the function x8(ln(x)) as follows.Redefine the function as follows.

Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

Q: 2) Find the first derivative of y = sec1(2e3*)

A: To find the first derivative of the given function.

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

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

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Q: Find the derivative of the function y = 1/ln(1 − 7x)

A: