Differentiate each of the following function with respect to x. f(x) = e*" (In 4x) f(x) =(cos 2x)' c) (Use Product Rule) d) (Use Chain Rule) e) S(x)=; +4e0x e St

Q: f(x) = acos(b\x) x2 COS

A:

Q: 1 FIND THE DERIVATIVE OF EACH FUNCT'ON. 1.) y= sin () a.) y= Tan( 3x) 3.) y= Cos( 3

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use mathematical induction to prove that the derivative of f (x) = xn equals nxn−1 whenever n is a…

A:

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

A:

Q: Find the derivative of the following. Ax) = (x)sin x h(x) 1+ csc x 1- csc x

A: Given : f(x)=(x)sinx h(x)=(1+cscx)/(1-cscx)

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (2…

A: Given function is   Differentiating both sides with respect to x, we get

Q: Find the derivative of: 9e 7sin ( 3x*) Use e^x for e". -

A: We use chain rule to find the derivative.

Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

A:

Q: Find the derivative of k(x) = log3(x) cos

A:

Q: 1. Compute the derivative of f(x) = arcsin(x² e³*).

A:

Q: I. For y 'logarithmic differentiation'. e3" In a find an expression for dy as a function of x using…

A: This question is related to differentiation, we will solve it using given information.

Q: 14. f(x) =(In x)* 3. 15. Н(х) 3D

A:

Q: The derivative of In (cos x) is

A:

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

A: We have to find the derivatives of the following function: y=sin 4x3+3x+1 We know the formula of…

Q: f(x) = In (3x + e3x)

A:

Q: Find the derivative of cos(3x) O -3sin(3x) O 3sin(3x) O 3cos(3x) O -3cos(3x)

A:

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Use the basic definition of Cosh to find the derivative of the function, Coshx=ex+e-x2. Find the…

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: Differentiate the following implicit function with respect to x: xy² -;=- cos (y?) a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

A:

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: Find the derivative of function.

A: To fFnd:  Derivative of y=ln 4ln3x

Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

A:

Q: Discuss the relationsh ip between the derivative dy/dx and(lim) with drawing if it is required

A: See the attachment

Q: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y =…

A: given y=cos9θ+41

Q: (1+x²-1) y = tan²¹ / √₁+x²

A:

Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

A:

Q: g(x) = cos ¹x+ 1-x

A:

Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: find the first & second derivative of fox)=e 2. Cosx.

A: Given: The function fx=x2excosx, To find: First and second derivative of given function fx.

Q: what is the first derivative of cosx^2(x^2+2)

A:

Q: Differentiate the following implicit function with respect to x: xy - -- cos (y*) a.

A: Solving the first part: Given:

Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |

A:

Q: Y= In (In2 (1-x))re?

A:

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

A:

Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

A:

Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

A:

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

A:

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

A:

Q: Compute the derivative of f(x) = arcsin(x² e3=).

A:

Q: Find the derivative of each function 2 sin x 5x3 1. h(x) = In x -3e* h(x) = 2 cos x g(x) : 1+7x

A:

Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

A:

Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

Q: Find the derivative of the function. 8 f(x) =x" log 6x .7 ,7 O A. X +8x log ,x .7 O B. In 6 + 8x log…

A: According to product rule of differentiation ddxuv=vddxu+uddxv and according to power rule of…

Q: 1. Find by implicit differentiation for xe = 2xy + y³.

A:

Q: Compute the derivative of f (x) : = arcsin(x² e³«).

A:

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

A: