Use the product rule to find the derivative of a function in the form f(x)g(X)h(x) Question For k(x) (3a223) (x - 2)(-x + 3), find the derivative of k(x) using the product rule = Select the correct answer below: 3r417 312 21 16 6x-2 -6x 2 O 1823 18224-11 12T3 512 62x 27

Q: I need help with 61. I am integrating with partial fractions.

A: Take the constant out.

Q: 2.5 Can you show me the steps to solve the problem? Directions: Find the derivative of the function....

A: Here the given function is y = (cosx) /√1 + sinx . and we find the first derivative of the function:...

Q: F(x)= ( x^5-4x^3+x)^-5 Find derivative

A: Given,

Q: A rock is dropped from a height of 64ft. Its height above ground at time t seconds later is given by...

A: Consider the model function that represents the height above the ground as s(t) = –16t2+64, where 0≤...

Q: Points A and B are separated by a lake. To find the distance between them, a surveyor locates a poin...

A: The diagrammatic representation of the given problem is, 

Q: What is the domain of the function: f(x) = 1/(1 - 2 cos x)?

A: Given, 

Q: Write the function below in the form P=P(0)at. Is this exponential growth or exponential decay? P=4e...

A: To determine the base of the given exponential function.

Q: Calculus Question

A:

Q: The island of Manhattan was sold for $24 in 1626. Suppose the money had been invested in an accounte...

A: From 1626 to 2012 is (2012-1626)=386 years 

Q: Consider the following function:  f(x,y) = (xy (x2 - y2)) / (x2 + y2), (x,y) ≠ (0,0),               ...

A: we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify...

Q: How do I integrate a fraction where there is a monomial in the numerator and a binomial in the denom...

A: In order to integrate the rational function whose numerator is monomial and denominator is binomial,...

Q: Solve the given differential equation by undetermined coefficients. y''' − y'' − 25y' + 25y = 3 − e...

A: Given Differential equation is

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

A:

Q: Find a general formula for f.(n) f(x)=9x2ex Talking about formula to find any derivative I asked thi...

A: Given function:

Q: Form polynomial function f(x) with real coefficient having given degree and zeros. Answers vary depe...

A: It is given that, degree = 4, zeros are 3+2i and 4 and multiplicity is 2.Since the degree is 4, ther...

Q: See attachment

A: Consider the given triangle ABC.

Q: Find the y-intercept of the tangent line to y=(-1.7)/(sqrt3+8x) (The denominator is all under the sq...

A: Given, 

Q: Find the equation of the line that is tangent to the curve y=3x cos x at the point (π,−3π).The equat...

A: Given that

Q: 10 the function f is defined by f(x) = x°(x + 7)4 For 11 On which two intervals is the function incr...

A: Given function

Q: A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 2 feet lo...

A: Given thatLength of water trough is 8 feet and cross section is equilateral triangle with side 2 fee...

Q: Find an equation of the tangent line to the graph of the function at the given point. y = (e4x − 4)...

A: We first have to find y'We apply exponent rule and chain rule.y'= 8(e^(4x))*(e^(4x)) -4)

Q: I need help on my Calculus HW. I am suppose to find the limit for question #49 in Section 3.3 (page ...

A: Consider the given limit function.

Q: We say a function f is even if f(x)= f(-x) for all x in its domain. We say f is odd if f(-x)= -f(x) ...

A: Given,

Q: find the equation of the tangent line for the given f(x) at the given point f(x)=(1+1/x)4, (1,16)

A: Consider the given function:

Q: Differentiate the following function y sec(0) (0 tan(0))

A: The given function is,

Q: Can you help me with this problem step by step?

A: Consider the given function.

Q: Solve the differential equation by variation of parameters. 4y'' − y = ex/2 + 7

A: Result used:

Q: Answer question 14

A: The given expression is 8x2 – 16x + 6.

Q: Find the derivative of the function.. 8 7 h(x) 218 4 х - h'(x)=

A: To find the drivative of the given function y=h(x)

Q: See attached

A: Given function,

Q: Show the solution

A: Given differential equation is

Q: Can you help me with this problem step by step?

A: Given equation is

Q: See attachment

A: The length of the ramp is 13 ft and the height of the platform is 10 ft.

Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,...

A: To determine the intersection of the line with the coordinate planes.

Q: Can you please do number 12 and show the steps of the y and x intercepts

A: Given function is

Q: Find an equation of the tangent line to the curve y=sin(3x) + cos(4x)   at the point (pi/6), y(pi/6)...

A: Given equation is y=sin(3x) + cos(4x).

Q: Use linear approximation, i.e. the tangent line, to approximate as follows: Let f(x) = and find the ...

A: We find the equation of tangent at point a=1, by using formula

Q: When a rocket is 10 kilometers high, it is moving vertically upward at a speed of 1000 kilometers pe...

A: To determine the rate of change of angle of elevation with respect to observer.

Q: Find the matrix A of the linear transformation T from ℝ2 to ℝ2 that rotates any vector through an an...

A: The transformation T  rotates any vector through an angle of 150 degree in clockwise direction.

Q: Can you help me with this problem step by step?

A: The given equation,

Q: Find the second derivative. f(x) = 5e−x − 3e−5x f ''(x) =

A: Recall the following facts.

Q: = -21e 2 C D +4 D +9D t1o)y 4. /f x-O -4 l 10

A: To sove the initial value problem for y=y(x)

Q: Examine the graph of f(x) = 2*. у 1 1 1 2 a. Use the graph to explain why, for h > 0, a+ h) - f(a) h...

A: Using the formula we find f'(a) and simplify it.

Q: Use the definition of the logarithmic function to find x. (Simplify your answer completely.) (a)    ...

A: Part (a): ln(x) = - 5 Use the logarithmic definition: if

Q: Differential Equation Show a comple te solution 11 2X 2-y-ay e t2

A: Firstly, we find complementary function by solving auxillary equation

Q: Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 8 centimeters...

A: We need to calculate the rate of change of level of root beer in the conical cup, dh/dt.We know that...

Q: Find the two x values at which the tangent line to the curve y=(x+3)/(x+2) is perpendicular to the l...

A: Compute slope of the given equation for general x.

Q: When a rocket is 6 kilometers high, it is moving vertically upward at a speed of 100 kilometers per ...

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: In 1993, the moose population in a park was measured to be 3590. By 1997, the population was measure...

A: Let x represents the years and y represents the moose population . Lets assume the year 1990 as x=0....

Q: If tanθ=6/13, and if cosθ<0, the... secθ= cosθ= sinθ= sin2θ= sinθ/2=

A: Since, tan of an angle is positive and cos of the angle is negative, so angle lies in second quadran...