For the f(x) = 1/1-X^2 and g(x)= x^2/1-X^2 A) shows that these functions have the derivative B) what does this imply about the relationship between these functions ?

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: Consider the function f(x) whose second derivative is f”(x) = 10x + 8sin(x) If f(0) = 2 and f’(0) =…

A:

Q: Prove, using the definition of derivative, that if f(x)  = Cps x,then f'(x) =- Sin x

A: Given fx=cos xBy definition of derivativef'x=limh→0 fx+h-fxhfx=cos xThereforef'x=limh→0 cosx+h-cos…

Q: 1. Use one of the definitions of the derivative at a point to determine the slope of the tangent…

A: f(x)=2x2-x We need to find the slope of tangent at the point (1,1)

Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

A:

Q: 2.) Compute for the derivative (DO NOT USE THE DEFINITION) of A. 2x3 y = tanh sin x2

A:

Q: Suppose that the function y in the Derivative Product Rule has a constant value c. What does the…

A: Derivative product rule:The derivative product rule for the functions x and y is given by,

Q: Find the derivative of f(x) = √x^2 + 1 at a = 2, using the limit definition (i.e. first principles)

A:

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the…

A:

Q: Find the derivative of g(x)= (x+1)/(x+2) using th limit definition.

A:

Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

A:

Q: tan2 (3 + Ax) – tan2 3 lim Ar 0 Ax

A:

Q: What is the derivative of f(x) g(x) in terms of f and g? Compute the derivative of -sin(x) · 2x=1…

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

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: How do you find the derivative of f(x) = 5 using the limit definition of derivatives? I know it is…

A:

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: derivative of g(x)= intergral from 1 to root x, (z^2)/z^4+1

A: ddx∫1xz2z4+1dz

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

A:

Q: Find the derivative of f (x ) =V sech( In (8x + 1)) - sech(In(8x + 1)) tanh( In(8x + 1)) A 2/ sech(…

A:

Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

A:

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

A:

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

A:

Q: The derivative of f is equal to f'(x) = f(x)f(-x). Show that f' is not one-to-one. %3D

A: First we will find 1st derivative using the given relationship.

Q: 2. Find the derivative of f(x) = -4x2 + 3x + 2 from first principles (i.e. the limit definition of a…

A:

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: We want to use the Richardson method to calculate the first order derivative antisymmetrically at…

A: We need atleast 2 points to calculate the Richardson second order derivative. The small parameter…

Q: Find the derivative of the function f(x)=1/x using limit definition derivative

A: According to the given information it is required to calculate the derivative of the function using…

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

A:

Q: Find the derivative using the long method 3-t to

A:

Q: 16. r(0) = sec 0 tan 0 – 2eº -

A:

Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

A:

Q: On which open interval is the derivative positive/ negative .

A: Given:

Q: Find the fourth derivative of f (z) = 57 + In (z) – 109z. Enclose arguments of functions in…

A:

Q: The value of the second derivative of at its point of inflection is A less than zero B equal to zero…

A:

Q: Find the derivative of f(x)= 11x^2 at x=1 please use definition of derivative formula

A: Given :   y = 11x2    at x =1

Q: Find the equation of the tangent line of f(x)=2x^2-4x+1 at (2,1) using the limit definition of a…

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

A:

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…

Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

A: