Find y as a function of x if x²y" – 3xy – 12y = x², y(1) = -7, y(1) = -7. y =

Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: Find y" by implicit differentiation. x² + 5y2 = 5 %3D

A:

Q: Find the differential of the function y=(3-x8)1/2

A:

Q: Find the derivatives of the function x²(xy² y)² = x² - y² )

A:

Q: Find the derivative of y with respect to x. (Hint: chain rule) y = -csc-1 24 V(8x + 92 - 9 24 (8x +…

A:

Q: Use the Chain Rule to find the derivative. y = (t2 + 3t + 1) -5/2

A: Here given y = (t2 + 3t + 1) -5/2

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Use implicit differentiation to find y' for xy-3x-4=0 y- y's E your and ww

A: To find y' by implicit differentiation, (without expressing y in terms of x)

Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4…

A: Given:        y= x+12x2+1-3

Q: compute the derivatives indicated. f(x, y) = 3x²y – 6xyª, and ax2 ay2

A:

Q: Determine the differential of y for the function y=3ln(4x2).  Simplify fully.

A: To Determine: Differential of y

Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: Find the derivatives of the functions in Exercise

A: Given: r=21θ+θ We know that ddxxn=nxn-1                                                        ..1

Q: Find the third derivative of ƒ (z) = ¥9z +I. f" (2) =

A: Answer is mentioned below

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y

A: Given that a function f(x,y) is continuously differentiable on an open region, we can derive the…

Q: Use the chain rule to find the derivative of f(z) = 4(4z5+5z“) i

A: Given : fx = 44x5+5x4-12

Q: Find the second derivatives:y^n for y=1/8x^4-1/3x^3+3/4x^2-3x+5 And f(x)=2x/5x-2

A: (i): Given : y=18x4-13x3+34x2-3x+5 f(x)=2x5x-2…

Q: Find the third derivative. 1 (x + y)Z + (x – y)Z = a

A:

Q: What is the derivative of y + x + y² = x ? O y : 1- 3z2 3y2 + 2y 1+ 3x? 3y? + 2y O y = 1- 3x2 3y? +y…

A:

Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

A:

Q: Find the derivatives of the functions in Exercise

A: Given: y=x2+1x+5+1x Differentiating y with respect to x, dydx=ddxx2+1x+5+1x+ddxx+5+1xx2+1…

Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: 9x= (Jx+ x) (+xt) %3D

A: Given  g(x)=x+x2x3+x+2 To take derivative of g(x), we apply product rule (uv)'=u'v+v'u…

Q: Find the derivative of the function Z=3t^(11/3)-2t^(9/4)-t^(1/2)+1

A:

Q: Find the derivative of the function f (x, y, z) = -9x + 5y – 10z at the point (-3, 6, 5) in the…

A: we have to find the following . I have explained in details please see the explanation and if any…

Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

A:

Q: Find the two first-order derivatives of the function f(x, y) = 2xy² – x² +y* You must show work.

A: ∂f/∂x = fx(x,y) = d/dx [2xy2 - x2 + y4]                       = 2y2 - 2x ∂f/∂x = fx(x,y) = 2(y2 -…

Q: Find the derivatives of the functions in Exercises 27. y = x2sin^2 (2x2)           28. y = x^-2sin^2…

A: To find derivative of 1) y=x2sin2(2x2)2y=x-2sin2(x3)

Q: Find the derivatives of the functions in Exercise

A: Explanation: Given that,  w=(2x-7)-1(x+5)     Formula used: According to the product rule of…

Q: What is the derivatives of f(x)=(x^3)/(9-X^2) and its x and y intersect?

A: a) From the given problem: fx=x39-x2Ory=x39-x2   So,   dydx=ddxx39-x2=ddxx39-x2-ddx9-x2x39-x22…

Q: Find the first and second derivatives of the functions w = 3z2e2z

A: Given:Assuming the given function is:

Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

A:

Q: Calculate the second derivative of the function y = f (x) defined by the equation x³ + y +3xy + 3y²…

A:

Q: 2. (x² – y²)³ = 3a*x? %3D

A: The given equation is x2-y23=3a4x2 We have to find the derivative of y with respect to x. In this…

Q: 2. Find y' by implicit differentiation. (1) xy-3x+2x =8 (2) 9x² +4y² = 25 (3) x²+2xy- y² =5 2 3 = 6…

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

Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

A:

Q: y 3 + 4x-1 = 8y¬1

A: Using differentiation formula:ddxxn=n.xn-1

Q: Find the derivative of the function. y = (3x + 1)°(x+ - 6)° A y=(32x +9)(3x +1) (x*-6)° B y' = 9(3x…

A:

Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

A:

Q: Let f (2) = (4z + 3) (i – 2). What is the real part of the derivative f' (1+ i)?

A: A complex-valued function consists of two parts. The part without i is referred to as the real part.…

Q: Find the first and second derivatives of the function.

A:

Q: Find the derivative of the function. 9+4x - 8x y = y' =D %3D

A: We obtain the derivative of the given function y by using the quotient rule of differentiation. We…

Q: Find the derivative of the function. u(x) = (x2 + 1)9x2 − 1 u'(x) =

A: The function u(x) is:

Q: Find the derivative of the function. y = (3x+1)(x*-6)s O a. y' = 9(3x+1)2(x+-6)°+32x(3x+1}³(x4-6) а.…

A:

Q: Find the function whose derivative is Inx+1. A) xlnx B) x+xlnx x+1/x D) x+Inx

A:

Q: find the first and second derivatives w = 3z-2 - 1/z

A: Consider the following equation: w=3z-2-1z Differentiate w with respect to z:…

Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

A:

Q: Use implicit differentiation to find ∂z/∂x and ∂z/∂y if 3x2+4y2+2z2=5

A: Given ,       3x2+4y2+2z2=5

Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

A: