Let G(x) = f f(t) dt and H(x) f(1) dt where fis the function graphed below. Graph of f

Q: dx Evaluate f- +1) using the Cauchy principal value.

A:

Q: A graph of y = f(r) is shown. In the same coordinate system, sketch a graph of the derivative…

A: To draw the graph of the derivative of the function

Q: Find the derivative of the function rsin(x) 1- t2 dt. 1+t4 g(x) /1

A: Explanation of the answer is as follows

Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: Find all the second-order partial derivatives of the functions w = x2 tan (xy)

A: Consider the given function: Here the objective is to find all second-order partial derivatives of…

Q: Find the partial derivative. f(p, q) = ev af

A: From the given problem; fp,q=e6pq As we know that: The chain rule: fgx'=f'gx·g'x The Power rule:…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = / 1 -dt 1+ t…

A: We will find f'(x) as following.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) e2t2…

A:

Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: COE Compute the mixed second order partial derivative of z =

A:

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

A:

Q: Determine the signs of the partial derivatives for the function f whose graph is shown below. (a)…

A: We have determined the signs of the partial derivatives for the function f for the given graph.

Q: If f is a function of three variables that has continuous second-order partial derivatives, then…

A: This question  is based on a simple theorem

Q: Q6. Find the first derivatives by using chain rule of the following functions: i. f(x) = tan %3D ii.…

A: Given that:                       (i) f(x)=tan1x(ii)g(x)=lnx3+x-1

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

A:

Q: Show that the function f(x) = 1/2 e−|x|IR(x) is a valid pdf.

A: Let the function is given by, fx=12e-x      for Rx Further we simlified it as, fx=12ex      for…

Q: Compute all second derivatives of f(1.y) = (x+) e- %3D

A:

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: 1 Let f(x)= J. dt. Find the derivative f(x). -dt. t4 +5 e2x none of the choices

A: Use the concept of derivative of an antiderivative and simplify.

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(*) = Ve…

A:

Q: Find all second-order partial derivatives for the following. f (x, y) = 2y ln x

A: To find all the second order derivative for the function f(x, y)=2ylnx

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 1/x h(x) =…

A: Here I am attaching image so that you understand each and every step.

Q: Use the chain rule to find the derivatives of f(x) and g(x) as well as f'(0) and g'(0): f(x) = (2x³…

A: According tp our guidelines we can solve only one question so we are solving 2nd question for you.…

Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: Find the first partial derivatives of the following function. f(x,y)%3D2x

A: Given,  f(x,y)=2x8y

Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

A:

Q: Calculate the derivatives of all orders: f'(x), f"(x), f'(x), f(4)(x), ., f(n)(x), .. .../ f(x) =…

A:

Q: g(=) = / Compute the derivative of g(x) dt. -2xe5 - 2xe - 2xe

A: Given           g(x) = ∫x21et3 dt

Q: A graph of y f(x) is shown. In the same coordinate system, sketch a graph of the derivative function…

A: In the interval -4,-1, the function is decreasing giving a negative to positive slope.

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: se Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function g(x) : I VR+…

A:

Q: let the pdf f(x) is even function then E(x) is?

A: We know, F(x) is even, Than, F(x) =F(-x) From definition, For even function ( if minimum = - n, than…

Q: Find the derivative of the function In t dt.

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. '6 G(x) :…

A:

Q: Sketch the graph of a twice-differentiable function y = f(x) that passes through the points (-2, 2),…

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) =…

A:

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: NOTE: Refresh your page if you can't see any equations. . the given graph is a parabolic graph and…

Q: Find the partial derivative of fy for the function * 3 f (x, y) = (3x² + y²) ³ 3x² (3x² + y²)²…

A:

Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = 3t…

A: By fundamental theorem of calculus, we have

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: Find all the second-order partial derivatives of the functions w = x sin (x2y)

A: Given function is w=xsinx2y. To find all the second-order partial derivatives of the function.…

Q: g(e) = . Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.…

A:

Q: Find the derivative of the given function a. F(x) = dt 1+ b. g(x) = [ - dt sinx 1+1*

A:

Q: 11. 2008 BC #92 Lety be the function with first derivative defined by f'(z) = sin2) for 0 sxs 2. At…

A: