For items 3 to 8, consider a continuous function y=f (x) whose first derivative is y'=x(x– 2).

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

A:

Q: Find the derivative of the following function with respect to x. /5x + 8 1 – 9 cos (4.x) - h (x) =…

A: The given function is:hx=5x+8 1-9cos4x3x2+10x4 This function can be written as: hx=5x+812…

Q: Find the derivative of the following function. 7x e y= In 4x y =D

A:

Q: For which of the following functions would the quotient rule be considered the best method for…

A:

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 11) y = In 1-x (x +4)3

A:

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: In the given question as follows, find the derivative of the function. y = e√x

A: Solution: Consider the given function is: y = ex Differentiating with respect to x we have dydx =…

Q: Find derivatives of the functions defined as follows:

A: Given: fx=ex3x+2

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A:

Q: Find the derivative f(x) of the following function with respect to x m 2 fm(x) = Σ n n=1

A:

Q: Find the derivative of the functions below: In(x) (a) g(x) = log,(x) g'(x) = (b). y- in(6x®)

A:

Q: Evaluate the derivative of the following function at x=0: f (x) =(e"+x)+ 4 O 16

A:

Q: The second derivative for the following function at x = 2 f(x) = V2x + is O 1 O 1/4 O 1/2 3/4

A:

Q: Suppose that the only information we have about a function f is that (1) and the graph of its…

A:

Q: ) For each of the following, use the product rule to find the derivative function. d) f(2) = +1 x2…

A:

Q: What is the Derivative of the following function; y = e-xsinh x

A: Our Aim is to find the derivative of y=e-x sinh(x)-(i)

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A:

Q: Compute the derivative of the following function. f(x) = 8x e 2x f'(x)= ]

A:

Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

A:

Q: Prove each of the following using the definition of the derivative.(a) The First-Power Rule: d/dx  x…

A: Let f is a real valued function. The derivative of f is defined by: f'(x)=limh→0 fx+h-fxh provided…

Q: Find the derivative for each function: g(x) = In ( e^x / 1 + e^x )

A: Our Aim is to find the derivative for function given below:-g(x)=lnex1+ex -(i)

Q: Compute the derivative of the following function. f(x) = 11 e 4x f (x) =

A:

Q: Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist,…

A: Given fx=x+223

Q: Find A and B given that the derivative of Ax? + B, x –1 is everywhere continuous.

A: Given function is f(x)=Ax2+B,x<-1Bx5+Ax+4,x≥-1 We have to find the value of A and B  so that the…

Q: Given the function y=(2x+1)3(x−1). Find all derivatives of the nth order from n=1 to n=5.

A:

Q: For each of the following functions, find the indicated derivative using the definition. 1. f(x) =…

A:

Q: Use the table to the right to find the given derivative. 1 2 3 4 f(x) 1 3 4 d f'(x) 3 1 4 2 dx

A:

Q: Find the derivative with respect to x of each of the following: 5. f(x) = (2x + 1)e-*-1 xe" +2y²ln x…

A:

Q: d -y(x) if e²-y = sin a d.x

A: We will solve the following

Q: 1. For the following functions y=f (x), find f ' (a) by using the definition of derivative at a…

A: Here we use the definition of derivative.

Q: Verify that each of the following difference approximations for the first derivative provides the…

A: As each approximation has independent of previous one . So according to guideline , I am verifying…

Q: The only function whose derivative is itself is y = e*. a. True b. False because y = 2ex is another…

A:

Q: I need the third derivative for all of the following functions: f(x)= + 1 + x

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: For each of the following functions, find the derivative (dy/dx) with respect to x: 7. y = cos x 9.…

A: The given functions 7. y=cos x8. y=ex9. y=ln x we have to find the derivative of this functions.

Q: Find the derivative. F'(x) if F(x) = (e×" + 1) °

A:

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: 6. v(y) = In (y² – 8y – 1)

A:

Q: Find the derivative f(x) of the following function with respect to x: fm(x) = > n=D1

A:

Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: 9. y =cosx nth derivative and n is divisble by 4  it means n is even number 4,8,12...ny so lets…

Q: Use f'(x) = lim **n)=l to find the derivative at x for the given function. h h-0 s(x) = 8x +7 s'(x)…

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: Find the derivative f (x) of the following function with respect to x: 2 fm(x) = Σ n* · x" n=1

A: We havefm (x) = (∑n=1m nx xn)2 We expand this series : fm (x) = [1x+2x x2 +3x x3+4x x4+......+mx…

Q: Which of the following functions would produce a derivative containing an x 5/3 term? O a) y = x 8/3…

A:

Q: Find the derivative of the following function. f(x) = ..... 3x e dx -X +2

A:

Q: Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not…

A: f(x)=cosπx2

Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): x²(x + 1),…

A:

Q: Find the derivative of the function by the limit process. h(s) = −2√s

A: h(s) = −2√s