A function that converts dress sizes in the United States to those in Europe is given by D = f(x) = 2x + 24 where x is the size in the United States. a. Find the European dress size that corresponds to a U.S. dress size of x = 10. D = b. Find the function that converts European dress size to U.S. dress size. x = f-'(D) = c. Use part b. to find the U.S. dress size that corresponds to a Europen dress size 46. x = Question Help: M Message instructor Add Work Submit Question

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: What is the derivative of the function f(x) = 2x + 3 at the number x = 4?

A:

Q: Find the slope of the secant line to the function f(x)=x3 when x=1 and x=2.

A:

Q: Find the second derivative of the function. Fx) = x In VR) + 9x f"(x) -

A: Answer and explanation is given below...

Q: Use the Generalized Power Rule to find the derivative of the function. h(z) = (8z2 − 6z + 7)4

A: Given function is as below

Q: F(X) = X + よ2 %3D

A: Given, fx=x+3x2

Q: Find the derivative of the function. f(x) = (9x2 – x) In(x) f'(x) =

A:

Q: Find the derivative of the function. F(x) = (3x6 + 4x3y4 F'(x)

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use the first derivative test and the second derivative test to determine where each function is…

A: The given function y=3x+4 Differentiate with respect to x f'(x)=323x+4 f'(x) is not defined at…

Q: Find the derivative of the function. F(x) = (x* + 3x² – 2)*

A: Use chain rule to find derivative of given function as shown in step 2

Q: What is the slope of the line tangent to the graph of a function defined by f(x)= x² + √x at x=1?

A:

Q: Use the definition to compute the derivative of the function f (x) = Vx2 + 1.

A: We have to find derivative

Q: The number of licensed drivers in a country (in millions) can be approximated by the function g(x) =…

A: Solution: The objective is to estimate and interpret the value of the derivative in 2014.

Q: Use the product rule to calculate the derivative  f(x)=x^3(2x^2+1)

A:

Q: p(4)(x) = (x² + 9)² f(6)(x) =

A: Given: f""(x)=(x^2+9)^2

Q: Use the definition of the derivative to find f fx) = 2/(x + 3)

A:

Q: Use the definition of the derivative to solve.

A: Given,

Q: For the function f(x) x + x3, find all of the relative and absolute extrema using the first or…

A:

Q: compute the derivative f (x) = 7−2x

A:

Q: Why can't the power rule be used to differentiate the function y = e"?

A: Given

Q: Use the Product Rule to find the derivative of the function.

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx The quotient rule of…

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: 6. %3D F(x) = 5x

A: f(x)=65x

Q: Use the Quotient Rule to find the derivative of the function. x2 h(x) = %3D X + 2 h'(x) =

A:

Q: Find the first and second derivatives of the function. (6t2 - 4)2 (5t2)

A: Given function: f(t) = (6t2 - 4)2 (5t2) = (36t4 - 48t2 + 16) (5t2) = 180t6 - 240t4 + 80t2 Recall the…

Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

A:

Q: Find the derivative of the function. f(x)= (x2+6/x)5

A:

Q: Why can't the power rule be used to differentiate the function y = = e"?

A: Because the power rule only works for function raised to a power for example x^3,x^8 etc.. it is not…

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: Considering f(x) = 9 – 5x. To find the approximate derivative of f(x) at x = 2.

Q: f (x) = 5x* f(x) %3D 12x5—4х4

A:

Q: the derivative () of = f(x) = 2

A: Please refer to the image below

Q: Find the derivative. h(x) == 2* %3D

A:

Q: F(x) = X2

A: Consider the function: fx=x2 The derivative of f(x) with respect to x is the function f′(x) and is…

Q: If an object moves along a line so that it is at y=f(x)=3x2−2x at time x​ (in seconds), find the…

A:

Q: How will you differentiate an implicit function that can't be expressed in the form of y = f(x)?

A: For the differentiation of implicit function, we will differentiate each side of an equation with…

Q: Find the derivative of the function. f(x) = X + 8

A: Here, we need to find the derivative of f(x)=xx3+8. So,          f'(x)=xx3+8' Apply the Quotient…

Q: Find the derivative of the function. F(x) = (4x + 4)3 (x² – 5x + 4)4 %3D F'(x) = %3D

A:

Q: Find the derivative of f(x) = x ^2at x = 3.

A:

Q: Find the derivative of the function. 9. f(x) =X x+8 f'(x) =|| %3D

A: Given: fx=x31-6x+8

Q: Find the derivative of the function f(x) = x2 -8x +9 at the number a

A: The given equation is f(x)=x2-8x+9 The derivative of the function is the rate of the change in the…

Q: F(x) = Vx +3x %3D

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Use the definition of derivative to find f (x) if f(x) = Vx+3.

A: fx=x+3

Q: Find the derivative of the function. f(x) = ( x/√x + 5)3

A: It is given that,fx=xx+53. We have to find the derivative of the function.

Q: Find the derivative of the function. F(x) = (9x6 + 4x3y4 F'(x) =

A:

Q: Use the definition of a derivative to find f(x). 7 (x) (x) =

A: we have given f(x).  We have to find the derivative of f'(x) by definition of derivative

Q: with positive exponents only

A:

Q: Find the derivative of the function f(x) = e8+5x³. O f'(x) = 8+52³ O f'(x) = (8 +5x³) e³+5x³ O f'(x)…

A: To find derivative f'(x)

Q: Determine the derivative function for f ( x ) = 6 x^3 + 9 − 7/x^2.

A: Consider the given function. fx=6x3+9-7x2 The objective of the problem is to find the derivative for…

Q: A company has a stock valued at A, in millions of dollars, that changes at a rate given by dA dx =…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.