3. If f(x) X-x find F(tanx) 1+x2

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

A:

Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

Q: . Use the definition of the derivative to find f'(x) given f(x) = x + Vx

A: Given,         fx=x+x

Q: Find f' (x) for 8 sin(x) f(x) = -; 7x2 – 8 sin(x) s'(x) = |

A:

Q: If 1– cosh x f(x) : 3+ cosh x then f'(x) =

A: The quotient rule of the differentiation uv'=u'⋅v−u⋅v'v2.

Q: 26. Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = {Z 1 if x = 0…

A: Given f(0)=1 now we have find   limx→0f(x)=limx→0(sin2x2x)=1  ( By property)

Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: -x² +1 Let f(x) be defined as f(x)={* - | 1–sin² x if x20 if x<0

A:

Q: On the graph of f(x)=tanx and the interval [0,2π), for what value of x does the graph meet the…

A: x 0 π4 3π4 π2 π 5π4 3π2 7π4     tanx 0 1 3 ∞ 0 -1 -∞ -3

Q: Let f(x) = x cos(3x). Find f' 3

A:

Q: If f(x)=tanh(3x)f(x)=tanh(3x) then f'(x)=f′(x)=

A:

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: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

A:

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

A:

Q: Find the linerization  of f(x)=x^3  near x=1 . use that linerization to approximate (1.1)^3

A: Linearization of f(x) near x=a is given by f(x)=f(a)+f'(a)[x-a] Where f'(x) is first derivative of…

Q: Find f(x) if f "(x) = x -cos x, f ' (0) = 2 and f(0) = -2.

A: To find f'(x) from f"(x), we will integrate f"(x) c=integrating constant Given f'(0)=2 , using that…

Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: If f(x) = 4x sin-), find f'() = f' (0.4) -

A:

Q: ,for x 1 Discuss the contuniuty of f andf'.

A:

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: If f(x)=tanh^-1 square root x to the fourth power then f'(x)=

A:

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: How would you find f '(x) baased on knowing f(x)= (4 tan x)/x?

A: Given function is f(x) = (4tanx)/x. Differentiate with respect to x as follows.

Q: Suppose f''(x) = -(sin(x)), f'(0)=6 and f(0)= -1 Find f(π/2) =?

A: Given query is to find the value of the function at indicated point.

Q: On the graph of f(x) = tanx and the interval [ − π, π ), for what value(s) of x does f(x) = 1?

A:

Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Let f(x)= x2 + sin x - 2 cos 2x. Find (f-1)'(-2)

A: Given: fx=x2+sinx-2cos2x To find: f-1'-2 Now, we know that f-1x' = 1f'f-1x

Q: Find f'(0) if f (x) = In(cos .x).

A: we have to find f'(0)

Q: Find the equation of the tangent line to the function f(x) = In(5x) at x = 2. (Use symbolic notation…

A: Given that, f(x)=ln5x To find the equation of tangent line to the function f(x)=ln(5x) at x=2.

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

A:

Q: Find the equation of the tangent line to the function f(x)=6^x at x=2 (Use symbolic notation and…

A: At x=2  y=62 =36 So the point is (2,36)

Q: Find f'(x) where f(x) = x*in(#) + (sin(x))".

A: Given that, fx=xsinx+sinxx To find the derivative of this fx=xsinx+sinxx, take the logarithmic on…

Q: Could the limit as xà1 of f(x)=(x+sinx)/(1+x+cosx) be found simply by substituting 1 into the…

A: Given function f(x)=(x+ sin (x))/(1+x+ cos (x)) Now we will evaluate limit of f(X) as X tends to 1…

Q: 9) Find f(x) if f'(x) = 7 sin x + 2x - 3 and f(0) = -3

A: Obtain f(x) by integrating the given first derivative as follows.

Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

A:

Q: if f(x) = tan(3x) f’(x) = f’(5) =

A:

Q: 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

A:

Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

A:

Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

A:

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

A:

Q: Find f''(x) for f(x)=(tan(2pix))^3

A: From the given data:

Q: Find f'(x) for f(x)=tan^3x+tan(x^3)

A: The function is given by,

Q: 2) Find the derivative of the following func (c). f(x) = (x+ 7 sin z) (1 – 5 cos x) tanx (d). g(x) =…

A: We can find the answers as below.

Q: Determine whether f(x) approaches ∞ or – ∞ as x approaches -2 from the left and from the right. TX =…

A: Given figure To evaluate

Q: 3-Еxpand In [x' sin x /Vx2 + 1]

A: According to guidelines we should have been able to solve only one question at a time #3 expand

Q: 2. For f(x) = x tan-(x), find f'(x).

A:

Q: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

A: