5 tan x If f(x) then f'(x) = f'(4) =

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Derivative of In |x| Differentiate In x, for x > 0, and differentiate In(-x), for x < 0, to conclude…

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Q: 7. h(x) = tanx- tan 8. h(x) = 3 sec-x

A: we have been given the equations to differentiate w.r.t x

Q: Find the first derivative of g(x) = 2 ln(x)tan(x*). 2 tan(4) g'(z) = | 82 sec²(4) In(z)+ X syntax…

A: We will solve the problem. The syntax error is ln(x4)  instead of 'CAPITAL i'. Refer to the final…

Q: Find the derivative of the function by the limit process. Find an equation of the tangent line to…

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Q: sin x Find the derivative of y = tan with respect to x, by using the Chain Rule.

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Q: 3x y=3- + Arccos V8-x3

A: We have to find out the first derivative  .

Q: Find the derivative of f(x) = In [sin(x) +x] Lsin(x)-x] %3D 2(sin x – x cos x) x2 - sin? x )2(x cosx…

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Q: lim x-->0 (1+sinx)^(1/x)

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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: sin (2x) cos (2x) csc (x) 2. Determine the limit of · xVx4 as x approaches 0

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Q: (tan x) = fu. v dx = (sin x) = | -=-=dx = (cos x) = fe" dx = | (arcsinx) = sec x tan x dx = secx tan…

A: We have to find out derivative and integral

Q: 75. F(x) has a negative derivative over (-, 2) and (5,9) and a positive derivative over (2, 5) and…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: SIn (-x) In x if x 0

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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 derivative if f(x)= ((x/2) + (x √x))ex

A: The given function is fx=x2+xxex. Obtain the derivative as follows.

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: In(cos(x)) cos(In(x)) Find the derivative of cos(In(x)) – In(cos(x)) sin(In(x)) A cos (In(x)) -xcos…

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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: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: Differentiate the function. f(x) = sin(3 ln(x)) f ' (x) =

A: To find the derivative of the function

Q: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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Q: limit of x approaching 0 from the right of ((sin(x^2))^x )

A: Given   apply squeeze theorem

Q: tan hx tanh x sec hx-1 sec hx +1

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Q: Using Chain Rule method Find the derivative of: 5 2. F= x³ + x² + x + 1 1. F(x) = ln Cos(x²)

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Q: he value x = ! is a critical number of the function f(x) = x ln(x), which has x) = 1+ ln(x). Use the…

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Q: sinh x O Compute the derivative of f(x) = (cosh x)

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Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

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Q: Find the derivative of the algebraic functions f(x) = x (1-) x+3, : g(x) = x + cotx

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Q: 7. Find all relative extrema. Use the Second Derivative Test to identify the local extrema. 2 f (x)…

A: Given:The given funtion is f(x)=3x+2xTo findWe have to find the relative extrema of the…

Q: 2 sin(x)-sin(2x) х-sin(x) lim X→0

A: Given,           limx→02sinx-sin2xx-sinx

Q: Find the first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1-tanx 1. If f(x) = then find f'(-). 1+tanx

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Q: How to find the anti derivative of sin(x)/cos^3(x)

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Q: Limit Sin 1/x x -0

A: Answer is mentioned below

Q: 31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not…

A: Given: fx=x2+x     , x≤13x-2   ,  x&gt;1

Q: Find derivatives of the first derivative involving differences, products, and quotients. sin x 1- y…

A: As per Bartleby's expert answering policy, we can answer one question with a maximum of 3 subparts,…

Q: o( san(s) sin(2x) + lim X 0 cos (x) × 6

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Q: 1+sin 2 x Find the derivative of f(x) 2 cos3 x

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Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

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Q: The derivative of a function intervals is decreasing ? is given by f’ (x)=e^ sin x -cos x-1 for 0 <…

A: topic - decreasing intervals of a function f is decreasing on intervals where f'(x) is negative

Q: Given f(x)=x(x-1). a) Find first derivatives of function f(x) using product rule and chain rule.

A: Our objective is to find the derivative and critical points.