at main derivative rule does each integral bring to mind as you think of a Example S sin(t²) t dt d d cos(inside) = - sin(inside) · insi dt dt S(5m³ + 9)³ m² dm S cos(sin(4f)) cos(4f) df Se tan(5k-4) sec²(5k – 4) dk

Q: Find the derivative of the function. Simplify where possible. y = (tan-'x)? y = tan-'(x²) y =…

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Q: Arctan(x) ln(x^3 + 2) find the derivative    F(x) = arccos(3x^2) find the derivative

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Q: B) Derivative following functions by using chain rule method 1) y = 5u³- u? , 2x = 4u? 2) у %3D |1 ,…

A: Answer (1): Given that, y=5u3-u2, 2x=4u2 Suppose fgx Then, to find the derivative apply the chain…

Q: sinx is the second derivative of what funtion? coS X h. -cos x sin x d. -sin x

A: -sinx is second derivative of what function?

Q: Obtain the derivative dy/dx. y = 6x - 5x – 10 dy - 5 2 dx State the rules that you use. (Select all…

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Q: Find the derivative of the function f(x)= (2x^4- 5x^2 +1)^6 / sin(5x+1). What’s the value of f(0)…

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Q: 3. What is the derivative of y = (f(g(f(g(x))))? Furthermore, if you are asked to evaluate the…

A: The given function,     y=fgfgxg0=0, f0=1 and g1=f1=1

Q: 1-Vx Let f (x) = Which one is the derivative of f (x)? = COS 1+vx

A: Solution: The objective is to find the derivative of the given function

Q: Find any local extrema using the Second Derivative Test of f(x) = x²e-*

A: We will find f'(x) and equate it to 0 to find the extreme points and then check them at f''(x) to…

Q: sin(z) Find the derivative of the funciton F(x) = In(1 + 6v) dv. F'(x) =

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Q: Using the (limit) definition of derivative to show that the derivative of the function sin(x) is…

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Q: = * sin (t – 1) dt Find the derivative of the function g( x O sin (3x – 1) sin (2) 3 sin (3x – 1)

A: We will use Newton leibniz formula to solve this question.

Q: Compute the derivative of the function y = 7 sin-(x) at the point x 3 (Use symbolic notation and…

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Q: B) Derivative following functions by using implicit differentiation method 1) y+x-100= 0 2) x…

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Q: The second derivative of a curve C at any point is d2y/dx2 = sec2x tan x. If 2 is the slope of the…

A: Solution

Q: 8. What rule should be used in deriving f(x) = x³? A. Constant rule B. Sum rule 9. Find dy/dx y=e³x…

A: To find:  8. Name of the rule used in derivative of x5. 9. Derivative of e3x . 10. Derivative of…

Q: (c) Observe that the examples in (b) work nicely because of the derivatives you were asked to…

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Q: Find an equation of the tangent line at x = 0. y = x5 + cos(x) .13 (Use symbolic notation and…

A: We have given equation  y=x13+cosx Put x=0  y=0+cos(0)=1 Point on the curve x1,y1=0,1…

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable.

A: Given :                The function f(x) = 2 sin x + cos 2x over 0,2π To calculate :…

Q: Find the second derivative of f () = 6 sin (5z). Enclose arguments of functions in parentheses. For…

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Q: Find the slope of the tangent line to the sine function at the origin. (a) y 2 y= sin(x) 1 Зл 2 (b)…

A: we have to find slope

Q: Find the slope of the tangent line to the sine function at the origin. (a) y 2- y= sin(x) 37 2 EX…

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Q: Product Rule for the second derivative Assuming the firstand second derivatives of f and g exist at…

A: Given: The first and second derivatives of f and g exist at x

Q: a) Using the method of first principle find the derivative of the function 1 f(x) = Show that sin* x…

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Q: sin x COS X Show that secx = then use the identity to derive the basic integration rule sec x dx =…

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Q: Find the derivative of the given. f(x)= cos x cot x let g= cos x and h= cot x. Then, g'= -sin x…

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Q: Use chain rule to find the derivative of the function below: y = cot(t –) -10 y = E- 10) y = tan(5 –…

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Q: sin x 2. Find the derivative of y = 3+2cos x

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Q: III. Find the fifth derivative using product rule y = sin3xcos4x Where r is the last digit of your…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: sin 0.5 va Find the first-order derivative of y = at x = 2 and h = 0.2 a.) Forward difference b.)…

A: Three approximations to the derivative of function f(x) at x=k are 1.  the one-sided (forward)…

Q: The first derivative of the implicit function sin 2x = cos 2 A. -cos 2x/sin 2x B. cos 2x/sin 2x C.…

A: To find: The first derivative of the implicit function. Given: The given implicit function is…

Q: UnaUna f(x)=f x+1 Show all your work and simplify the result completely. Find the derivative of e…

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Q: Consider a function given by f(x) = -0.1x + 0.15x² – x + 0.8 Centered difference method…

A: In this we find the first derivative of the given function by using central difference method.and…

Q: Use logarithmic differentiation to find the derivative of the function. y = x7 cos(x) Step 1 Using…

A: Here, the given function is: y=x7 cos x⇒ln y=7cos x ln x

Q: dx as a function of x if dt Find dt2 x sin x. dt?

A: We will solve the following

Q: a sin (cos X) b cos (cos x) c sin (sin x) d cos (sin x) a By expressingy = x in the form y = sin…

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Q: sinz 3. а) Find the derivative of the function f(x)= [ (1-r²) dt using FTC-1. 3a. b) Verify the…

A: To find -  Find the derivative of the function fx = ∫cosxsinx1 - t2 dt using FTC-1. Verify the…

Q: 1. DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, 1. y = sin (x + 3x +…

A: d/dx(sinx)=cosx d/dx(xn)=nxn-1 d/dx(cosx)=-sinx

Q: A.x^3+xy^2=y^3+yx^2 Explain how to find derivative by using implicit differentiation please!…

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Q: 2. y = tan-¹(cosh x) (sin² x) (sech x) secx [use logarithmic differentiation]

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Q: Find the first derivative of the function 3 cos x y = x? sin(2e*)- ex Show all the works clearly.…

A: The given function is y=x2sin2ex-3cosxex.

Q: 7- cosh(x) 7+ cosh(x) Use appropriate rules of differentiation to find the derivative of Gx)

A: Quotient Rulefg'=f'g-g'fg2

Q: Use a computer algebra system to analyze the function over the given interval. 1 f(x) = sin(x) –…

A: To find the derivatives of given function

Q: The approximate value of the derivative of a function f(x) using centered difference approximation…

A: The derivative is the instantaneous rate of change of a function with respect to one of its…

Q: 5. (No Calculator. Show all your work) Find the derivative of the function. (a) f(x) = tan(x³) – cos…

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Q: The derivative of f(x) = ln(3 sin¬ x) is Select one: O None of the other options 1 O f' (x) = (sin-l…

A: We have to derive the given function.

Q: A. Using chain rule find the derivative of the following functions. 1) f(x) = (x³ + 3x²) 200 2) f(x)…

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Q: Find the indicated derivative. Find y " if y = 5x sin x. O y" = - 5x sin x y"= - 10 cos x+ 5x sin x…

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