2- Show that a(p) can be transformed to using the transformation: dx Y = а (p)dx Hint: Use chain rule.

Q: Find the first partial derivatives for f(x,y)= 9x cos (3xy). of dx

A: To find the first partial derivatives  f(x,y) =9x cos 3xy

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

A:

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given y=e5x-7 Let u=5x-7, then y=eu dydu=eu and dudx=5 Version 1 of chain rule is given by…

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: y=5x2+11x20Chain rule:dydx=dydu.dudx

Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = √u and u = x3

A: Recall the chain rule of differentiation:

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: The chain rules helps in finding differentiation of composite function. We call a function composite…

Q: If y = tan(4x + 1), determine using chain rule. dy dx

A:

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: To calculate the derivative of the given function using chain rule: y=3x2+7x10

Q: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A: To find: The value of dydx in terms of x and y. Given information: y=csct,x=sec-1t

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: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

A:

Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A:

Q: Find both first partial derivatives. z = cos(5xy) az ax az ду II II

A:

Q: Find the first partial derivatives of f(x, y) = 4x cos(x2 + y?). %3D

A: Given fx,y=4xcosx2+y2

Q: Find of/dx and dfldy. f(x,y)% 3 (3xy-1) of

A:

Q: Find the partial derivative. z = sin(2.a*y – 3xy?) az

A:

Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = u3 and u = √x

A: Given: ,and . Find out by using the chain rule.

Q: (c) Use implicit differentiation to compute dy/dx: In(xy) = x°y² + e"

A: We have to find the dydx.

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: use the chain rule to find dy/dx for the followingy=sin^2 (3x-2)

A: Firstly, we introduce two new functions u(v) and v(x) as shown on board.

Q: Use chain rule to find given x² + 2y² + z² and x os (st), y %3D Cos

A: Solve the following

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

A:

Q: Find both first partial derivatives. z = cos(10xy) az ax az ||

A:

Q: H (w) s (+リ? (outて)

A: The given problem is to find the inverse Fourier transform of the given function, we have to split…

Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

A:

Q: 94. Find dy/dx if y - 2 by using the Chain Rule with y as a com- position of a. y- u' and - V b. y -…

A: a) Given y=x32 The chain rule state that dydx=dydu·dudx

Q: use Gamma Function to evalute the Rollowinq e dy

A:

Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx) y = (tan x + sin…

A: The given function is y=tanx+sinx-3 We have to find dydx by using Leibniz’s notation for the chain…

Q: -32e* – 140 -dx J e2x +9e* + 20

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: 2] write the chain rule formula for the derivatives Of and E , where Z=ZCrisit).

A:

Q: Find all Second partial derivatives fcx.y)- Sin?Cmx+ny)

A: Given that, f(x, y) = sin2(mx + ny) we have to find second partial derivative with respect to x and…

Q: 3) Find dy given 3xy = In x. dx

A: Given  3xy=lnx To find dydx   implicit differentiation is used Both sides have to be differentiated…

Q: t seel dx

A:

Q: Show X -メ+1 =ソ- Can be reduce d to homegenons equation 2X +y-! メ+ 2y t1 dy dx

A:

Q: chain

A:

Q: Find both first partial derivatives. z = cos(x2 + y2)

A: Given , z=cos(x2+y2)we have to find the first partial derivative

Q: Use chain rule and compute dx/dv if z=x2+xy3, x=uv2+x,w3, y=u+vew

A: Here, the given functions are: z=x2+xy3,x=uv2+w3,y=u+vew So, z is the function of x and y and x,y…

Q: If z = sin(x/y) and x = ln (u) and y = v^4, find the partial derivatives of z with respect to u and…

A:

Q: y' – ey : = sin x

A: In this question, we have given a differential equation y'-ey=sin(x) here, we need to check either…

Q: Draw the slope field for Y - 2y dx

A:

Q: Draw a slope field for dy/dx= -6x^2/y.

A: we have to draw a slope field for dydx=-6x2y

Q: b) Use implicit differentiation to find dy/dx of y² : X-1 x+1

A: Using implicit differentiation & quotient rule.

Q: Find all second partial derivatives of Z e

A:

Q: 1 B3. Evaluate dx, using substitution method.

A:

Q: Find the partial derivative of the given u = In[x?e*Y].

A:

Q: Find dy/dx of the following function using Chain Rule. y=(-3x5 +1)3

A: we use chain rule for differentiation y=(-3x5 +1)3 dy/dx =3(-3x5 +1)2(-15x4) dy/dx = -45x4(-3x5 +1)2…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.