71. Prove that if f is an exponential function, then f'(x) is proportional to f(x).

Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x?

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Q: Find the function whose derivative is 1-e2x

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Q: sketch the shifted exponential curves

A: We have to sketch the shifted exponential curves: y=-ex and y=-e-x. We know the graph of ex and e-x,…

Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

A: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

Q: Suppose we want to use logarithmic differentiation to calculate the derivative of y=x²x . As a first…

A:

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

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

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Q: Find the thousandth derivative of  f(x)  = x e-x

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Q: (4) Use logarithmic differentiation to find the derivative of the following function. y = x¹/x

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Q: Which function has the same derivative function f (x) as g(x) = lnx + x² – x?

A: we have to find derivative

Q: Determine the first derivative of the ff. function y = ln| le* – 1/

A: We have to find the first derivative of the function: y=lnexex-1 We know the property of logarithm,…

Q: 3 7 - use logarithm differentiation to differentiate to find y prime (dy). y = x

A: The given function is, y = x.Take log on both sides of the function.

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

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Q: Suppose that 50,000 bacteria are in a dish and that the population grows continuously by 4% each…

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Q: x+1

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

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

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Q: f (x) = ln(x · 5*)

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

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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: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: If f(x) and g(x) is any function then, If limx→∞f(x)g(x)=∞ then f(x) grows faster than g(x). If…

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

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

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

A: Given function

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: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: )=1/x. Using this, compute the

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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: 1 Find the function whose derivative is (x+1)-

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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: a.) z= 5.

A: We will find the second derivative of the given function in the following step.

Q: 11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f = 0(g) and g…

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

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

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Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: X In Зх +1 y y' X

A: Given ; ln(x2/(3x+1))=y/x.

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=lnx,  gx=ln2x

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.

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

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Q: What is the derivative of the exponential function a x, a >0 and a ≠ 1? What is the geometric…

A: The derivative of the exponential function ax is as follows.

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: 24. Find the first order derivative with respect to x of the function u = log(x+ x .

A: The solution for the above question is as shown below.

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

A: Topic = Derivative