2²y. 3. Consider the function f(, y) =

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: Find the directional derivative of the following function at P(1, 0) in the direction that produces…

A: Given  fx,y = -3x2+4y3+2xe32y

Q: Find the derivative of the function. 8y9 y= In V+9 6.

A: The solution are next step

Q: find fxx(x,y) and fxy(x,y) derivatives for the following function z=f(x,y)= e^x^2 +y^2

A:

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

A:

Q: 8 Find the derivative of the function: 1) g(x) = V1+ t² dt 2) g(x) = d 3x 1 1+4 3) g(y) = , tsin2tdt

A: Apply lebneitz integral rule

Q: 4. Compute the derivative, r'(t), of r(t) = (2t°, v2t, 2 –t=2).

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: 9) Where is the function h(t) = (t + 5)"3 differentiable?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

A:

Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

A:

Q: I the second derivative of the function F(t) = 7tsin(º). ver F"(1) =

A:

Q: Find the derivative of function defined as follows. p(z) = z(6z + 1)4/3

A: Given function is pz=z6z+143. To find the derivative of the function. Solution: Power rule of…

Q: C. Find the third derivative of the given function/s. 3. у %3D х (2х + 1)2 4. у %3D (2х— 1)(х + 2)2

A:

Q: 1. Find the derivative of the following function. 4. f(w) = 3D 6w* +3w +2w f'(w) = %3D

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

A:

Q: Let f(4) = 1 and f'(4) = 5. Calculate the following derivative. %3D d f(Vx) dx %D

A:

Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

A:

Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

A:

Q: = x³y² – 3x²y + 5x – 3y + 12

A:

Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

A:

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

A: Given:Assuming the given function is:

Q: If we use trapezoidal rule for a function f(x) = x +2 1 - , then the approximate of J f(x)dx is…

A:

Q: Find the derivative of function defined as follows. s(t) = 12(2t4 + 5)3/2

A:

Q: 3. find the second order derivative 어: Xt xy t y= 16 2 4.

A:

Q: 3 (a) Find the derivative of the function y = (t3 + 1)10 dt

A:

Q: Suppose that g(x, y) = xf(e"v´). Find g„, 9y and gyæ in terms of the function f and its derivatives.

A:

Q: Find the following derivatives of f(x,y) =2yey. f,x, y) = ,6, 9) =| fa(x, y) = fylx, y) = %3!

A:

Q: Find the derivative of the following function: 2x-1 11. y = %3D Sx +2 13. y = V2x + 6 %3D

A:

Q: Find the first and second derivatives of the functions s = t2 + 5t - 1/t2

A:

Q: 32. Differentiate the following function with respect to y. e + 3º = 1

A: This is a simple differentiation problem

Q: Find the derivative of the given function.   f(z)=−1/z^4.1

A: Recall the rule for differentiating powers when the exponent is a positive integer

Q: 2. Find the derivatives of the following functions as specified: a. h (2) = (9z +4), b. g (x) = (æ²…

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

Q: 2. Let f(x,y)= xe" and find a) fu. fy» fy

A: Please refer the attached image for complete solution.

Q: Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph of,…

A: To find the gradient of the tangent line of the point (5,1) on the graph of x+xy+2y2=12 Formulae…

Q: I. Find the derivative of y with respect to x. Use the given relation in its implicit form. d?u 3.…

A:

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: The objective is to find y'(2)and find the equation of tangent line to y(x) at x=2.

Q: 3) Use the definition to find the derivative of f(t) = +1 t+1 %3D

A: f'(t) = -1/t2

Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe

A:

Q: Q3. Find the derivatives of the functions 2x + 5 a) y b) w = (2x – 7)(x + 5) Зх — 2 5x + 1 с) и 2 Vx

A: We have to find the derivative of the following functions a)  y=2x+53x-2 b) w=(2x-7)-1(x+5) c)…

Q: Under what conditions is a linear function f(x)=mx+b,m≠0, a linear function?

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

Q: 1. Find the stationary points of the following functions. (a) f(x,y) = x²y+ 2y² – 2xy + 6 - (b)…

A:

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: For which values of a e R is the function ++(). f(a + iy) = (a²z - ary) + i + ay an entire function?

A:

Q: B) Find the derivatives of the following functions 2) y=2 Vx-1 sec Vĩ 2 (x+1)10 (2x+1)5 7) y=ttanh…

A: