Find the total differential of the function z = y³x³ + 15y + 14. dz = Now calculate Az and dz for x = -2, y = 4, and f(-2.01, 3.97). Enter Az and dz without rounding off. Also show the work requested below. Az = f( ) − ƒ( ) ≈ [ dx = dz = fz( and dy = ) dx + fy( SO )dy =

Q: Evaluate the derivative of the given function for the given value of x. y = 8x + 8 , x= 8 OA. V72…

A: Given function is Differentiating with respect to x by using chain rule of differentiation, we get…

Q: 1. y = Vz + 3z – 1

A:

Q: Find the derivative of the function y defined implicitly in terms of x. 7xy³ + 2x³y: 2x³y = 1 dy dx…

A:

Q: Evaluate the following. Show your solution 1. S5V dx. 3x² – 2x + 1 dr. 2. 3. SxV3x dx. SxV3x dx.

A:

Q: compute the derivative y = t−7.3

A:

Q: V3x – y + 6x*y? = 9y - 4.

A:

Q: Exercise, find the higher-order derivative. Given Derivative s(x) = 3x2 + 7x + 1 %3D

A: Introduction :

Q: Find all second order derivatives for z = 7ye4x. Zxx 0 Zyy = 3xy=2x =

A: The function is given by z = 7ye4x To determine: The expressions of zxx, zyy, zxy and  zyx.

Q: 2x+5 e. y = 3x-2 f. y = (2x? + 2)(x² + 3)

A: Derivative of the function y=f(x) is the measure of rate of change of y with respect to x.…

Q: Find the derivatives of the functions s =√t/1 + √t

A: The function is s=t1+t.   Differentiate the function with respect to t.…

Q: Find the derivative of the given function. y =x² Vx-

A:

Q: ind the first and second derivatives of the function. 1+ 12z W = (8-z) 4z dw dz dz? 2.

A: Topic:- derivatives

Q: (x² – y²)² – 4ay³ = yCosx + xCosy = 1

A: We have to find the derivative of the above functions .

Q: Find the derivative of the given function. y= 6x (7-6x)6 dy dx

A:

Q: 6. y = v4 V1 – 2v3

A: Solution is given as below: