Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 + 3x + 1). Find f′(x). b.) . Let g(x) = sin (cos x). What is g′(x)? c.) Suppose f(x) = (sin(2x) + 1)7 .Find f′ (π/2) and f′(π).

Q: Find the derivative of f (x) = /csc(e*+1) - 2e Ax + !csc?(e4x +1) (A csc(e4x+1) 'esc²(e4x+1) 2e tx…

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Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

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Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

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Q: compute the derivative. c(t) = 1-li – e2'k - e2

A: Given  ct=1ti^-e2tk^

Q: Find the derivative of f(x) = In(e +4) 1 O 3e? e+4 3e3

A: We use the chain rule

Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

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Q: Find the derivative of the following: 1. y=x(V1- x³ ) 1+x 2. у-. 1-x (x³+5) V4-x² 3. у — x*-x2+6 sin…

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Q: Find the derivatives of the following functions; (a) f(x) = In(2r² +1) (b) g(x) = x² In 2r (c) y =…

A: We have to find the derivative of given functions.

Q: Find the derivatives of the functions in Exercise

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Q: 1. Calculate the derivatives of the following functions. a) f(x) = In (In(x)) 4x3 b) g(x) =…

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Q: Find derivatives of the functions defined as follows:

A: Given: fx=ex3x+2

Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

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Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: Use the appropriate form of the chain rule to find the derivatives. 7x2 + 7y? + z²; x = psin ø cos…

A: This question is based on Partial derivatives.

Q: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…

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

Q: Use the appropriate form of the chain rule to find the derivatives. 5x2 + 5y? + z2; x = p sin o cos…

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Q: Q6. Find the first derivatives by using chain rule of the following functions: i. f(x) = tan %3D ii.…

A: Given that:                       (i) f(x)=tan1x(ii)g(x)=lnx3+x-1

Q: 10. Find the derivative of the following function. [Hint Using Chain Rule] a) F(x) = (x³ + 4x)? -5x…

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Q: Let y = (x + sin(x))³. Find g(æ) and f(x) so that y = (f o g)(x), and compute the derivative using…

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Q: 1. Find the derivative (dy/dx) of the following functions: In a) y = 3x7- 7x³ +21x2 In b) y = (x2 +…

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

Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

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Q: 10. Find the derivative of the following function. [Hint Using Chain Rule] a) F(x) = (x³ + 4x)7 d) y…

A: The chain rule says:ddx[f(g(x))]=f'(g(x)) g'(x)=d[f(g(x))]d[g(x)]·d[g(x)]dx   Note: According to the…

Q: Which of the following shows how to find the derivative of f(x)? 3e* f(x) |3D ex-7 (ae(*-7) -…

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Q: (b) Noting that f'(x) is also another function of æ, what is the linear approximation of f'(x) in…

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Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Suppose that the function f(x) and its first derivative have the fol- lowing values at x = 0 and x =…

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Q: 1. Find the derivative of each given function with respect to x. (i) F(x) = | t dt 1+ t2' (ii) G(x)…

A: FUNDAMENTAL THEOREM CALCULUS If f(x) is continuous over the interval [a,b] and the function F(x) is…

Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: Given function: gx=4e3x5+2x Differentiate the above function w.r.t 'x' g'x=ddx4e3x5+2x

Q: 15. Find the derivative of each of the following functions. TE-2 dt (a) f(x) = /" eV7t-2 %3| (b)…

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Q: Obtain the derivatives of the following functions f(æ), using the Simple chain rule and enter your…

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

Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

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Q: Use the chain rule to find the derivatives of f(x) and g(x) as well as f'(0) and g'(0): f(x) = (2x³…

A: According tp our guidelines we can solve only one question so we are solving 2nd question for you.…

Q: 59. Suppose that functions f and g and their derivatives with respect to x have the following values…

A: Since you have posted multiple questions i can do first question with first three subparts as per…

Q: Suppose that functions f and g and their derivatives with respect to x have the following values at…

A: Note: Since we are authorized to answer three sub-parts of a question at a time. And you have asked…

Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=

A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…

Q: 6.) Find the derivative of the following functions a.) f(x)=- 7-3х |t +1 b.) f(x)=. -1 c.) f(x)= ean…

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Q: a) If f(x), g(x) and h(x) have derivatives when asxsb. Show that there is a value c of x in (a,b)…

A: Consider a function f(x) such that (i) If f'x exists for every point in (a,b)  (ii) fa=fb Then there…

Q: Find the derivative of the following: 1. D, (x³) 2. D, (5x2) 3. D, (x – 2x*) 4. D, (x-2)(2x +3) 5.…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: Let y = (x + sin(x))³. Find g(æ) and f(x) so that y = (f o g)(x), and compute the derivative using…

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Q: Compute the derivative d/dx of the following functions: f(x) = x cos^2(4x)

A: The given function is: fx=xcos24x   As we know that; The Product rule: f·g'=f'·g+f·g' The Chain…

Q: The derivative of the function y = In (* + 1) (* - 1) is O y = O y = :- - 1 e+1 + -2 +1 ||

A: Question is solved.

Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Find the derivative of each function e 2x a. f(x) = 2x+1 b. f(x) = In Vx + 2x %3D c. f(x)= x?e* – 6x…

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Q: Let y=(x+sin(x))^5 Find g(x) and f(x) so that y=(f∘g)(x), and compute the derivative using the…

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Q: 7. Consider the function f(r) = In r - 4VT. 1- 27 (a) Show that the derivative is f'(x) :

A: lnx-4x

Q: Find the derivatives of the following: f(x)=e^2x-2e^x+1/e^2x-1   And  y=e^cos(r^2cos^2r)

A: Given ,f(x)  = e2x-2ex+1e2n-1

Q: Use the appropriate form of the chain rule to find the derivatives. W = 5x2 + 5y? + z²; x = p sin o…

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Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Find the third order derivative of y = In(cos(2x)). A. y' = -40sec? (2x)tan(2x) B. y' = -80sec?…

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Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

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