37. DETAILS HARMATHAP12 9.5.005. Find the derivative, but do not simplify your answer. y = (5x6 – 3x* + 2x² – 1)(4x° + 3x? – 5x2 + 3x) %3D - - y' = Need Help? Read It | Talk to a Tutor Submit Answer

Q: 3n If the normal to the curve y = f(x) at the point (3,4) makes an angle with the positive x-axis, 4…

A: (a) Normal to the curve y=fx at the point 3,4 makes an angle 3π4 with the positive x-axis then we…

Q: (1) Using the definition of derivative, find the derivative of th following functions: (a) y = xvx²…

A:

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

A:

Q: Find the values of x where the tangent line to the 1 graph of f(x) is parallel to the line - y = 8x…

A: Given: Graph of function fx=1x  and line y=-8x+4.

Q: Find the derivative of y=(e^2x)sin5x   (Not sure what to do with the (e^2x))

A:

Q: 5. By calculating a derivative, determine whether the following statement is true (or false): et et…

A:

Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

A:

Q: 5. Write the equation of the tangent line to the curve of y = e³x + cos(-x) at the point (0,2).

A:

Q: Find the equation of the line tangent to the graph of y = 3x cos x at the point (π, −3π).

A: Given Data: Equation: y=3xcosx Point: (x1, y1)=(π, −3π) The derivative of the given equation of…

Q: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

Q: 4) Use the quotient rule to find the derivative. Simplify the result. d dx |3x – 4

A:

Q: what is the derivative of arctan(u/1+4u)

A: To determine the first order derivative of the provided function.

Q: Consider the graph of y =JX) shown below in blue. Submit your answer to this question by completing…

A: To approximate the tangent line to the function.

Q: 9. 4x + 3y = In(4x – 3y); y %3D

A: Given:            4x+3y=ln4x-3y Find; y'           ddx4x+3y=ddxln4x-3y Apply the sum rule:…

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

A:

Q: 5) Find an equation of the tangent line to the curve y = sin²(x) cos(x) at the point (,0).

A: Slope of tangent,m  = dy/dx Equation of tangent to curve at point (x,y) y -y1 = m (x -x1 )

Q: Q2) Apply the differentiation rules to find the derivatives of: Inx 5 (a) y=x*.e*+2- Inx- cosx (b)…

A: Solve the following

Q: 2) Find the equation of the tangent line to the curve y = cos(2x+ at x =

A:

Q: Q2/ Discuss the relationship between the derivative and (Lim) with drawing if it is dx required ?

A:

Q: 14. The first derivative of y = arcsin4x is а. -4 b. -4 C. d. V1- 16x? VI- 4x2 V1– 16x? /1– 4x* -

A:

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

A:

Q: When a question asks to compute dy/dx using the definition of the derivative, how do I approach it?

A:

Q: Q1. By using the “definition of the derivative" find of y = v2x? %3D dx

A: Explanation and solutions is given below....

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

A:

Q: Give an equation for the tangent line to the graph of y = k(x) at the point when x = 2.

A:

Q: Does the graph of Sxsin(1/x), x + 0 g(x) 1o. x = 0 |have a tangent line at the origin? Give reasons…

A:

Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

A:

Q: 5-Find the equation of the tangent to the function y = sin x at x = n/4

A: Given :y = sinx

Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: |1+cosx, dr 5. r = 1-cosx' dx

A: Trigonometric identities: cos2x=1+cos2x2sin2x=1-cos2x2cotx=cosxsinx Differentiation formula:…

Q: Vt – 2. a²y y =t2 - 3' dx² X = %3D

A: Given functions are: x=t-2y=t2-3 Then we get, dxdt=ddtt-2=12t-2dydt=ddtt2-3=2t Therefore we have,…

Q: # 49. y = 2x arccos r -2/1- x2

A: Given y=2x arccosx-21-x2

Q: Find the derivative of y with respect to s. (56° +3) У3 sec

A:

Q: Q3: find the derivative of the following: 1. y = lnx + √1-x² sech-¹x 2. y= sinh-1(tanx)

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the derivative of the function toy do not nad to Sumplity your answer y= e* In (2)

A:

Q: Q3)B/ Find the slope of the tangent line to the graph of x² cos(y) = 2y- eš* at the point (1? %3D 00…

A:

Q: Find the derivative of y Cos3 3x+8 (x). %3D Provide your answer below: y = D

A:

Q: Find the 2nd derivatives of y with respect to x   lnxy=x^(2)+cosxy(Picture below for reference)

A:

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

A:

Q: Q3: find the derivative of the following: 1. y = Inx + √√1-x² sech-1x

A: I have given the answer in the next step. Hope you understand that

Q: ind the second derivative in its simplified form 2. y= 4 Arccos x/2 +2 square root of 4-x^2

A: Given, y=4arccosx2+24-x2

Q: The derivative of y = cos²x is %3D

A: Given -                  y= cos2 x . We have to find the derivative of y.

Q: FIND THE DERIVATIVE Of THE GIveM. FUMCTIC 3.) f(x) = Logio( ) %3D 8.) g= arccose-* 9.): y = qsin? x…

A: To find the derivative of the function7) fx=log10xx-18) y=arccosec-x9)y=9sin2x

Q: Q2 find the derivative of the following: 1) y = 2stn (5x) 2) y = Inxn cosh 5x ,3) xsin14y = y tan-4x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

Q: 3. Find Hhe to the (1,2) slope of the tangent live r=2-sin@ at the point curve

A: Then we plug this in the slope formula of the polar curve

Q: Find the values of æ where the tangent line to the graph of f(x) 1 is parallel to the line y = – 6x…

A:

Q: 3. Find the siope of the tangent line that crosses through the point (3, 7) along the 2 curve f(x)=x…

A: Given :f(x)=x2-x+1

Q: 13. Given the function f(x) = 4 + x? %3D Find the 8x + 2 equation of the tangent line to the curve 1…

A:

Q: 5 7. Find the slope of the tangent line to the graph of y = x² at the point where x = –

A:

Q: Which equation shows the correct derivative of the equation y = 2x² + 14x + 5? Oy = lim- 4th + 2h² +…

A: On solving this we will get that