81. y = f"(x) /

Q: h(x)=(x° +1} (2x+5)*

A: Given : hx = x2+132x+52

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: Use differentials to estimate the value of 7+(1.02) correct to four decimal places.

A:

Q: 3.

A: Indefinite Integration

Q: Find the derivative of x/ex^2.

A:

Q: what would be the output if the 2nd derivative is negative

A: We know that for a function y = f(x), the points of extremum are obtained if the first derivative of…

Q: what is the derivative of y=ex /(x2 + 15) Please show steps

A:

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

A:

Q: Use differentials to approximate the quantity   √17

A:

Q: In(x²) What is the derivative of

A:

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

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: When the graph of the derivative is positive then the graph of the antiderivative will be…

A:

Q: If the sign of the first derivative function is positive, the main function f(x) is decreasing.

A: We have to tell If the sign of the first derivative function is positive , the main function f(x) is…

Q: Determine the first derivative of the ff. function 1 + In(3x?) y : 1+ In(4x)

A: the given function is: y=1+ln3x21+ln4x we have to determine the first derivative of the given…

Q: The2nd derivative ofy = 24 is

A: USING LOGARITHMIC DIFFERENTIATION

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: бх + 5 -, is 10х + 8 The derivative of y =

A:

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: use differentials to approximate the change in y if x changes from 25 to 25.3

A:

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

Q: If f(x) = e cosT, the second derivative f"(x) is:

A: The given function is fx=ex cosx. Evaluate the first derivative of the given function as follows.…

Q: Find the derivative f(x)= In(ex+9)

A: find the derivative

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: Suppose that the revenue (in dollars) from the sale of a product is given by R = 70x + 0.7x² –…

A:

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

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

A:

Q: 7. Find the nth derivative of y = 1//x.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

A: To solve the following problem

Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

A:

Q: Find the derivative of n'n(cosu). Where n=666.

A:

Q: What is the difference of antidifferentiation and anti-derivative?

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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. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: Solve for the second derivative of the function below 3. у%3 (х— 5)*

A: Given: y = x-54 To find: Second derivative of the given function.

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: 4. Show that the derivative of log,(Va +5) is 3(r + 5) In(2)

A:

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: Find the derivative of y with respect to x for y=2x   ???

A: y=2x

Q: If 1 - + - and y(8) = , find y (8) by implicit differentiation. / (8) =

A: Given  1x+1y=2orx-1+y-1=2 Differentiate with respect to x

Q: the derivative of f(x) = xi at the point x = 4?

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: If y=x+ 4÷x+1 use the first derivative test to find where relative extrema occur.

A:

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: What is the average rate of change of f between x=3 and x=10

A:

Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

A:

Exponential Growth Model

The relation that represents an exponential function is: