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

Q: 2. Suppose, f'(x) =2 cosx+sec x, -7<x<: and it is known that f()= =4. Find the function f(x)

A:

Q: Suppose f"(x) = - (sin(x)), ƒ'(0) = –2, and f(0) = -3. %3D Find f(1/4).

A: Given,          Suppose f''x=-sinx , f'0=-2 and f0=-3.

Q: 3. Find the derivative of the following functions: a. f(x) = (x² + 1)(x³ – 2x² – 1) f(x) = b. 2 +…

A:

Q: If f(x)= cos (x)+3x , what is f'(x) ? COS O f'(x)=-sin (x) +3

A: First option is correct. Explanation is given below....

Q: If f (x) = cos(3x), then f' (-) is equal to

A:

Q: 2. Find the derivative of (a) f(x) = x4 +2x-2 + 4ex

A:

Q: 1 Find f"(x) for the function f(x) %3D (2+sin x)=

A:

Q: 1. Find the derivative of the following function: f(x) : (x² sin- if x ± 0 if x = 0

A:

Q: (1.8) Consider the function: { sin 2x if x # 0 In a if x = 0 f (x) = Write down the value of a for…

A:

Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

A:

Q: 18. f (x) = x3 − cos x

A: f(x) = x3−cos(x)d f(x)dx=ddxx3−cos(x)            =ddx(x3)+ddx(-cos x)            =3x2-ddx(cos x)

Q: Find a, b, and c for the function f(x) - a sin(bx- c) such that the graph of matches the figure. (x)…

A: Given  the given form of the function is fx=asinbx-c and the graph is

Q: Find the indicated derivative dz/do for z= x^3+x^2/1-x-4x^2

A: We have to find derivative

Q: 2. Find the derivative of the following functions: (5x+ 1)'(x + 3)5 cos°(x) sin°(x) (a.) f(x) = .…

A: Given f(x)=5x+77x2+35cos2x sin3x3   As per our guidelines we are supposed to answer only first…

Q: Find the derivative of the following. 2. g(x) = sin x tan x 1+sin x 3. h(x) = 1-sin x x+4 4. i(x) =…

A: 2.g(x)=sinx tanx3.h(x)=1+sinx1-sinx4.i(x)=x+4cosx5.j(x)=[(x2+cosx)(2x-sinx)]

Q: 4. Given that g(x) = x^4 + x^3 − 3x^2 + 2, answer the following. (a)  g"(x) =  .............. (b)…

A: We have,  gx=x4+x3-3x2+2              ⋯⋯1 (a) By definition of derivative, ddxkxn=knxn-1 On…

Q: If g(x)=cos2x and f(x)=sin (1/2) (π), find g(f(x))

A: Given functions are  g(x)=cos2x and f(x)=sinπ2

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

A:

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

A:

Q: 3sin-1x, if -1< x< 0 f(x) = x2+ Tt if x20 x+cosx'

A:

Q: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

A: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: -1 1 determine g (x) 18. For g(x)=sinx

A: Given,

Q: If f(x) = x² + cos(x), what is f" (x)?

A:

Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

A:

Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: Determine the concavity of the function f(x) = cos x^2 + sin x^2 + x^2 between x = -1.5 and x = -2.5

A:

Q: 1 Estimate the error if P3(x) = x - x³/6 is used to approximate the value of sin x at x = 0.1.

A: We have to find the error.

Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: If f(x) = 2 sin(x) + In(4x), find f '(x). f'(x) =

A: Given f(x)=2 sin(x)+ln(x) We know that d/dx(sin(x))=Cos(x) d/dx(ln(x))=1/x d/dx(xn)=nxn-1

Q: 1-Find the first derivative of the following function f( x) 5 cos (10x) + x' – 2x – 6x+ 10 For x=2…

A:

Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

A:

Q: 2 dx 5, is same as evaluating lim cos C+2+ F(<x))". Determine the value of f(x) if x=3.22 In…

A:

Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x…

A:

Q: Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)? What is…

A:

Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

A:

Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: Given the function xye9-sin² ecos² fxx of f is equal to 0. f(x, y)= The second derivative Select…

A: A detailed solution is given below. fx = partial derivative of f(x,y) with respect to x. fxx =…

Q: Find the derivative of the function ffor n = 1, 2, 3, and 4. sin x fx) = - (X), I n =4 Use the…

A: Solve for the derivative

Q: If f(x) = 3 cos(3 In(x)), find f'(x).

A: Consider the function  f(x)=3cos3ln(x)

Q: Find the extreme values for the function f(x) = x + sin x on the interval [0, 27).

A: This function is unbounded below and unbounded above, Therefore the function has no global extreme…

Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: The function f(x) sin x + cos x is an even function. True False

A:

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: If f(x) = 4 sin '(2), f'(x) =

A: The given function is f(x)=4sin-1x5  .................................... (1)

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: 1) 2 a) Let f(x)=√x +4. Use the definition of the derivative to find f'(x). Find f'(5) by two…

A:

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

A: