. Suppose you are writing an exam and you cannot remember whether the derivative of arcsin(x) 1 1 Explain how to use the domain of arcsin(x) to eliminate one of these is Vr2 – 1 possibilities. or VI- x2

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: 1. Can the graph of a function have more than one tangent at a given point? Explain by giving an…

A: Query- Can the  graph of a function have more than one tangent? Explain by giving an example and…

Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: Find the derivative of f (x) = -6 tan (x). Enclose arguments of functions in parentheses. For…

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Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin(x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: 1. Find the derivative of f(x) = tan³(sinx) + %3D

A: The given function isf(x)=tan3(sinx)+x3+3x4

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: f(θ) = 4 sin(θ) - θDifferentiating, we get  f'(θ) = 4 cos(θ) - 1 f'(0) = 4 cos(0) - 1 = 4 - 1 = 3y -…

Q: 10. g(x) = e*´ arcsin x

A: g(x)=ex2sin-1x We need to find the derivative of the given function.

Q: We cannot find the derivative of composed functions. We can however, using some algebra, find the…

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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: Find the second derivative of the function 2 f(x) = sin (3x). Show your work.

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Q: Find the first derivative of f(x) = e3r

A: To find the first derivative of fx=x3e3x. Solution: Quotient rule of derivative states that:…

Q: 1. If the first derivative is zero and the second derivative is positive, what can be concluded in…

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Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

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Q: tion of the tangent line to f(x) = 4 %3D

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Q: Find the derivative. Show your work 1. y=x^5 arcsin(x^3)

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Q: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

A: Given function: y=x-12x-x2-arccosx-1

Q: (8) Find the derivative of the functions (i)h(x) = sin 2.x cos 2x (ii) f (x) = cos (tan 4.x) 1 =-…

A: We need to differentiate the given function. We will use different method of differentiation . ( As…

Q: find the first derivative f'(x) at the point x 1.3. Use two point central difference

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Q: Find the derivative f(x) = [sin(4* + x)][cos(x* + 4) %3D

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Q: Find the derivative of y = tan 1 1-x -1 + sec Va +1

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Q: A. FIND THE DERIVATIVE OF EACH FUNCTION. DO NOT SIMPLIFY YOUR RESULT. et 17. f(x)

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Q: sinx 3. f(x)=(x)*

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Q: (5) Match the graphs of the functions to the graphs of their second derivatives. Original Functions…

A: Given: a function their derivative.

Q: Find the derivative of the function y = tan^-1 x/1-x + sec ^-1 sqrt x+1 %3D

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Q: Find the derivative of the function. (2) = earcsin(z) 3e arcsin(23)22 V1- 25 f'(z) = V1-26

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Q: · Find the DERIVATIVE of the given functions. Show work supporting your answers. (a) y = log2 (3x2 +…

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Q: What is the derivative of f(x) = tan-(x)? %3D

A: We can solve this as follows:

Q: (# 11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) =…

A: For the equation of tangent, we need to find the slope of the function at x=1.

Q: Find the derivative of: -2 sin (2x"). Hint: sin (x) = [sin(x)]...so use the chain rule (twice Submit…

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Q: (b) h2(x) = arcsin(Vr + 1). Hint: Use Derivative of sin-(g(x))

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Q: 3. Give the definition of a derivative of a function f of one variable at a point xo. /2 Find the…

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Q: Compute the derivative of the function y = 6 cos- (4x) at the point x = (Use symbolic notation and…

A: Solution ) y = 6 cos-14x Differentiate with respect to x  y' = 6 d/dx (cos-14x) [ we know that  d/dx…

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

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Q: How do you prove the general power rule of derivatives using the inverse property (x^n=e^(nlnx))?

A: The general power rule:

Q: , (a) Let f(x) = −x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A: The objective of the question is determine the equation of tangent line to the given function.

Q: Find the derivative of f(x) = (-x3 - 2x² - 2x) sin (x). Do not include "f'(x) =" in your answer.…

A: The given function is: fx=-x3-2x2-2xsinx   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Find the derivative of y = arctan(x² + 3)

A: To find: The derivative of y=tan-1x2+3. Formula used: Chain rule of derivative: fgx'=f'gx·g'x Power…

Q: Example38. From definition, find the derivative of cosx with respect to x.

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Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: Find the Derivative of the given function. If f(x) = -3, then f'(z) = %3D

A: Given f(x)=-3

Q: Find the derivative of the function. show all work y=(x-10)(x^2+2x) all over x^3

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Q: X-2 %3D

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

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

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: 5. Carefully explain why 2 arcsin(x)+2 arccos(x) : Hint: How can we tell a function is constant from…

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Q: Find the derivative of the function. f(x) = ln(4x² – 3x) - f'(x) = Preview %3D

A: Applying chain rule of differentiation

Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.