What is the domain of the function? g(x)=1/(1-tan(x))

Q: The derivative of the function f is defined by f' (x) = (x² + 4) cos (x - 3). If f(6) = -1, then use…

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Q: Find the derivative f(x)= (sin h^-1

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Q: Find the derivative of the trigonometric function.

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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. f(x) = tan-(3) f'(x) =

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Q: The derivative of the function has the same sign for all x in its domain, but the function is not…

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Q: Determine whether the point x=0 is an inflection point of the function f(x)=sinx.

A: Inflection point is the point on f(x) where the graphn changes the concavity. At this point  double…

Q: The derivative of the function f(x)=2xcos(x)-2 sin(x)is a. f(x)=-2 sin(x) b. f(x)=2x sin(x) c.…

A: ddx [ 2 x cos ( x ) − 2 sin ( x ) ]=?

Q: Find the derivative f'(x): f(x)=x4-x2+sin-1x/3 **4-x2 is under a radical sign!

A: Consider the given function f (x) taking (4-x^2) under the radical sign. Differentiate f (x) w.r.t x…

Q: Find the slope of the graph of the function at the given point.

A: We have the given function as fx=4x5+3x-sinx          ⋯⋯1 As we know that, slope of a function fx is…

Q: Find the derivative and simply. 1+cosx (a) f(x) = 1-cosx (b) f(x) = 3x5 cot-1 x

A: Part aGiven,          fx=1+cosx1-cosx

Q: Consider the function f(x)f(x) whose second derivative is f′′(x)=9x+10sin(x). If f(0)=3f(0)=3 and…

A: We have to find f(x) and find f(3) using given intial condition

Q: find all critical points of the function g(θ) = sin2 θ

A: Given Now, Critical points are points where the function is defined and its derivative is zero and…

Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

Q: Find the derivative  f(x)= sin 2xcos2x

A: The given function is,

Q: Find the derivative of the trigonometric function. g(x) = 8 tan(9x) g'(x) =

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Q: Let f (x) = sin−1(x^2/6)− tan−1(12x + 1). Find the derivative of f.

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Q: Compute the derivative. f (x) = sin2 x

A: First of all, consider the formula for the chain rule and the given function f (x). Then assume u…

Q: Differentiate the function. f(x) − x - 3 sin x

A: we have to differentiate the given function f(x) =− x - 3 sin x

Q: Let a be a real valued constant. Find the derivative with respect to x for the function f (x) =…

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Q: Find the derivative. g(x) = cosh(In(x)) g'(x) = ||

A: To determine the derivative of the function.

Q: Find the derivative h(x) = h'(x) = of the transcendental function. 14 sec x

A: The given function hx=5x-14sec x we have to find the derivative of h(x)

Q: Find the derivative of f(x) = Vx-7 tan-(x) + In a- 2.

A: We have to find the derivative of the function f(x)=x-7tan-1x+lnx-2.

Q: Find the point of inflection of the graph of the function. f(x)=sin x/2, [0,4 3.14]

A: First we will find it's first derivative then take first derivative is equal to 0 for finding it's…

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

A: Given the graph of derivative of f,

Q: In the given question, consider the function on the interval ( 0, 2π) (a) Find the open intervals on…

A: A function is increasing if the slope of the function is positive and decreasing when slope is…

Q: How is the graph of g(x)=2sin(3x) related to the graph of f(x)=sin x? GRaph the function g(x), show…

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Q: Find the slope of the graph of the function at the given point. f(x) = 4x5 + 2x - sin(x), (0, 0)…

A: We havefx=4x5+2x−sinx

Q: f(x) = -3 sin(x) cos(x)

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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 trigonometric function. f(x) = −x + tan x

A: Given: f(x) = −x + tan x

Q: 4. For what values of x does the graph of f have a horizontal tangent if f(x) = V3 x – 2 sin(x).

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Q: Find the slope of the graph of the function at the given point.                         f(x) = 4x5 +…

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

A: We can solve this as follows:

Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the…

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Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: Find the slope of the graph of the function at the given point. f(x) = 7x5 + 8x − sin(x), (0, 0

A: solution: the objective is to find the slope of the given graph

Q: f(x) = x' tan (5x)

A: Explanation and solutions is given below....

Q: Choose the derivative of tan-(x). 1 x /x² – I 1 1 + x2 1 V1 – x² - 1 1+ x2 1 /1 – x² | 1

A: Sex2x=1+tan2x

Q: Find a formula for (f-l)(x) given that f is one-to-one and its derivative satisfies the equation…

A: We can solve this using idea of function and definition of inverse of function

Q: What is the derivative of f(x) = (tan^-1)((3+x)/(1-3x))

A: Given:f(x)=(x+3)arctan(x)1-3xf'(x)=ddx(x+3)arctan(x)1-3x=ddx(x+3)arctan(x)·(1-3x)-(x+3)arctan(x)·ddx…

Q: Find the derivative of the function. f(x) = tan(5x²) %3D f'(x) = %3D

A: To find the derivative .

Q: Find the derivative  f(x) = cos-1(3x) sin-1(3x)

A: To differentiate the function with respect to x.

Q: ind the derivative of f(x)=(8-tanx)^(1/3) f′(x)=

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Q: (금) - Let f (x) = sin- tan-(6x + 1). Find the derivative of f. %3D f'(x) =

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Q: Find the derivative of the trigonometric function. g(x) = 5 tan 3x

A: Given that : The function is g(x) = 5 tan 3x .

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.