x2 1)Calculate the derivative using FTC(1): g(x) = ʃ  (t5 − 9t3 )dt                                                                          0                                                                                        5 2) Evaluate the following definite integral              ʃ  (x3+3x2 + 5) dx                                                                                                                                                                                                                      2

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

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Q: What is the derivative of y= 3Arcsin xº, 3 Arcsin x In 3 A y' = 1 - xa 3 Arcsin x* In 3 3 B y' : (а…

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Q: What is the derivative of y = x cos"'(x²)? dy (VI-2²' ) cos' z²+21² dz (VI-zª ) cos' z² –2=² (VI-z4…

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Q: In xy = x² + sin xy

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) At the point (, (2n…

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

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Q: Find the fourth derivative of f (z) = 37 + In(z) – 164z. Enclose arguments of functions in…

A: To Determine: find the fourth derivative of the function .  Given: we have a function…

Q: 2. Calculate the derivative of the following. А. y = (x* – 3x² + 5x) ³ DUKAS B. y = tan²(x² + 5x –…

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Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: i) Find the derivative of g(x)= 4x2 ii) If y³+2y-4x=5 find dy/dx cosx

A: Given: (i) g(x)=cos(x)4x2(ii) y3+2y-4x=5

Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

Q: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

A: Given: x2+y2=81

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: 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: Evaluate the derivative of a mq4.5.png cos (bvx ³) f(x) = a ln sin(cx²) if a = 107, b = 0.5, and c =…

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Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

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

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Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: Find the derivative of F(x) = 4 n sin(t) dt. %3D dx 3x² cos(x)

A: Integral calculus is one of the two main parts of calculus that is concerned with the study of…

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: Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y/x) + V3 sec-…

A: Given problem:-

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

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Q: How do you solve question 10?

A: Given function is  By definition of derivative , we have

Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x- (y/x) + V3 sec (2xy),…

A: we have to find directional derivative.

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x? – 1)³(x² + 3)? x3+4x…

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Q: Find the derivative of F(x) = n sin(t) dt. 3x2 d dx cos(x)

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Q: Find the fourth derivative of f (z) = 3* + In (z) – 191z. Enclose arguments of functions in…

A: To find :  Fourth derivative of function ,  f(x)=3x+lnx-191x

Q: Find the derivative of y with respect to > (x + 6) y = In V (x + 9)60 dy dx (Type an expression.)

A:

Q: 1. Find the derivative using differentiation rules: A) g(x) = 2x – + 3* - e x1 B) y(t) = (t³ – 7t2 +…

A: (1) (A)   ddx(g(x))=ddx2x-1x3+3x-e=2(1.x1-1)--13.x-13-1+3xln3-0=2+13x43+3xln3 (B)…

Q: ind the derivative of y with respect to x. y =-cos-16x + 7° 6 6. 1 + (6x + 7)2 81 - (6x + 7)2 O 4.…

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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: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: i. y = cosh(2x – 1) %3D 1 j. y = arccosh H| 8

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Q: Determine the derivative of y=tan(cos-'(4x)) -1 A y'= 4x2/1- 16x2 - 4x B y'= V1- 16x2 c) None of the…

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Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: What is the derivative of y = (sin (3x?)2? dy dr 12z sin' (3교2) VI-974 dy dr 12z sin (3z²) VI-9z4 dy…

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Q: 3. Find the derivative of (a) f(x) = (x+ 4 sin æ) (1 – 6 cos a), an (b) sin r g(x) %3D 6x

A: a). Given function is fx=x+4sinx1-6cosx. To find the derivative of given function. Solution: Product…

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

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Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

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Q: 1. Differentiate the function f(x) = (4x – 5)*(3x – 1)ª %3D d²y for y = 2x sin 5x dx? 2. Find dy…

A: It is derivative problem.