4. Find the first derivative of the given function using the Rules of Differentiation: а. h(x) — X-Vx b. y = e sin x 1-x %3D C. y= tan ("tan" x-9 2x-x-1 d. xy'+sec(xy) =5y e. y=csch(sin(2/x)) f. y (x)sin 5x

Q: find the derivative of y with respect to the appropriatevariable. y = sin-1 3/t2

A: We differentiate with respect to t using chain rule.

Q: Find the derivative of y with respect to the independent variable. y = 9cos zO O A. - 19cos AO In 9…

A:

Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

A:

Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: Find the derivatives of the functions  1. y = x2 cot 5x    2. y = x-2 sin 2(x 3)

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

Q: find the derivative (dy/dx) of the given function:  1. y= e^X sin X 2. y= (cos x)^9 3. 1/ ln(X)  4.…

A: Given,

Q: 1 Find the first derivative given that f(x) = xdx +

A:

Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

A:

Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: Find the derivative of y with respect to the independent variable. x2 y =log 8 Sx+1 1 8x+1 O In8 x2…

A:

Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

A:

Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Derive the formula dy/dx= 1/ (1 + x2) for the derivative of y = tan-1 x by differentiating both…

A: Given,

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: suppose that x and y are related by the given equation and use implicit differentiation to determine…

A: Given equation x3+y3=x3y3

Q: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

Q: 1. Find the second derivative of the following functions with respect to x. y = 3x2 + 5x - 1   2.…

A:

Q: Find the derivative of the function. f(x) %3D еx sec(9x) cos (9x) · e* + 7e* · sin(9x) f'(x) C cos…

A:

Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: (5) Find the derivative dy/dx, where: 4 1 -1 y=- y = cosec(cot3x), y=Vsinh¯3x 3 1+ cos° x

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

Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = x4/4 ln x - x4/16

A:

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: Suppose that x and y are related by the given equation and use implicit differentiation to determine…

A: →duvdx = udvdx + vdudx→dkdx = 0  where, 'k' is any constant.

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: 7. Jx+y +y² + x² = 18, y'at (0, 4 )

A:

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

A:

Q: 6. Let y + xy - y = 8x*. a) Find dy/dx using implicit differentiation. b) Find the equation of the…

A: In implicit differentiation, when we differentiate y, we use dy/dx

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: sin x 2x-x-1…

A: We have to solve

Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 dy dx b) EVALUATE THE DERIVATIVE FROM PART a AT THE…

A: Given: x4y3=-8

Q: 1. y = cos2(2x − 1)

A: " Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A: On simplification, we get

Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…

A: Given:- y = (-7x2-5x+5) (sin(x) +11x)  To find:- Derivative of y

Q: 10.Suppose that x and y are related by the equation 5x 2−4y 2=2 and use implicit differentiation…

A: The given equation is 5x2-4y2=2

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: find the derivative of y with respect to the appropriatevariable. y = 1/2 sinh (2x + 1)

A: We have to find derivative of y with respect to the appropriate variable: y=12 sinh 2x+1 We know…

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

A:

Q: Suppose ln (x + 2y) = x4.Use implicit differentiation to find the derivative of y with respect to x.…

A: Differentiate the given function implicitly as follows.

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

A:

Q: 1) Find the derivative of the function: (3х — 1)3 Vx* — 1 f(x) = cos² x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 11 with respect to x is The derivative of y = cos - 1

A:

Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

A: