Use differentials to give an informal justification for the chain rules for derivatives.

Q: Compute the derivative using derivative rules. y = (2e3x + 3e-2x)4

A: Solution:Given     y = (2e3x + 3e-2x)4 Formula:ddx(xn)=nxn-1ddx(eax)=a eax

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: Use the Chain Rule to express the second derivative off o gin terms of the first and second…

A: Let y=f o g then we have to find the second derivative of y.

Q: Find the derivatives of x^ x (x>0) with respect to x, find first principles

A:

Q: Find the derivatives of the functions in Exercise

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

Q: -a ; Y 5.)(*+y)² +(x-y)

A:

Q: Find the derivatives of the functions defined as y = -2ecot x

A: Given : y = -2ecotx

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

A:

Q: FInd the derivatives of the function f(x) from the first pribnciple  cos2x

A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: Find the derivatives of the functions in Exercise

A: The given function is u=5x+12x.

Q: Use the first principles of derivatives to find the derivative of y=5x-1

A:

Q: Find the derivatives of the functions in Exercise

A: The given function is y=x-35+π32

Q: use the Chain Rule to find the derivative. y = e2x2

A: To find the derivative of y=e2x2 using chain rule. Solution: Chain rule of differentiation states…

Q: Find the derivatives of the functions in Exercise

A: Find the derivatives of the functions in Exercise

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Compute the derivative using derivative rules.      y = (x 3 + 3x + 9) -4/3

A:

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function: y=etan t Differentiate the above function w.r.t 't' dydt=ddtetan t The function…

Q: Use the chain rule to find the derivative of lor67, 8x

A: To find the derivative of 106x7+8x6 using the chain rule. Solution: Chain rule of derivative states…

Q: Determine whether the following statement is true or false, and explain why. The chain rule is used…

A: Given: The chain rule is used to take the derivative of a product of functions.

Q: Find the derivative of 1-3)* (t3 -8) ,t # 2 2-t

A: Explanation of the answer is as follows

Q: How can the derivative function definition be applied to this problem?

A:

Q: 2х — 1 f(x) = 1-2х

A:

Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

A:

Q: Find the derivatives using the four step rule: f(x) = 1-x2

A: Explanation of the answer is as follows

Q: Use the Chain Rule to express the second derivative of f ◦ g in terms of the first and second…

A: First, find the first derivative of the function, consider that the function f(x) and g(x) are…

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

A:

Q: у %3D V1+ 2х (1 — х)-3

A:

Q: How do I find the following derivatives?

A: Using 1 rules of log 2 derivatives of composite functions (chain rule)

Q: The derivative of a function at each point is itself. y=kex

A: To find out the derivative of the function.

Q: Give information on this application of derivatives:  Optimization

A: Topic:- application of derivatives

Q: Find the derivative using the long method 3-t to

A:

Q: Find the derivative. Using Chain Rule y = (2x2 – 1)3(3x² + 1)³ |

A: According to question,Given Function,y = 2x2-133x2 + 13

Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: Find the derivative of dt

A:

Q: what are the real-life applications of derivatives?

A: Definition of derivatives helps to find real-life applications. Functions obtained after the…

Q: Draw the function x = 2y-y2 by using the tools of derivatives?

A: The given function isx=2y-y2.

Q: Can you please help me with derivatives and the power rule? I am struggling with that.

A:

Q: Find the derivative of the function. y = x²V25 - x² %3D %3D

A: Differentiate wrt x

Q: f(x)%3D (6- x²)3 — х? %3D

A: DIFFERENTIATION OR DERIVATIVE The differentiation is a process of finding the rate of change of one…

Q: find derivatives with different variables

A:

Q: (2x-6) ¹² 3. h(x)= (3 + نمو)

A: The objective of the question is evaluate the derivative of the given function.

Q: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

A:

Q: Find the derivative of y = x²( - %3D x2+1

A:

Q: Find the first and Secord derivatives of fanction

A:

Q: Define derivative, and identify the major types ofderivatives.

A: given,         define derivative, and identify the major types of derivative.

Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

A:

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: In x g(x) = 2

A: