For each of the following functions, find (f−1)′(a). 271) f(x) = x − (2 / x), x < 0 ,a = 1

Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

A:

Q: 2. g'(x) where g(x)= x² +7x-5

A: differentiation by using first principle

Q: 2x+1 S(x) = 3x+2,

A: Solution:Given     f(x)=2x+13x+23To find the derivativeFormula:ddx(xn)=nxn-1uv'=vu'-uv'v2

Q: The derivative of the function y= (z+7x)5 is O 5(2 + 72) (3z?+7) O 5(7 +7x) (3x² + 7) O 5(r +7x)*(3²…

A: Topic- derivative

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

A:

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

A:

Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

A:

Q: Solve for the derivative of the following composite functions. f(g(x)) = (x+ 4)* 2 f(9(x)) = (2x2 +…

A:

Q: For the function f(X) = ax3 +ba2 +cx, find the second derivative, f"(X). Here a,b and c are…

A: Given Function,F(x) = ax3 + ba2 + cx

Q: Find the derivative of function defined as follows.

A: Given: fx=82x2+5 Differentiating the given function fx with respect to x, f'x=ddx82x2+5…

Q: 2x+4 f(x) = (3x + 7) e.

A: Given query is to find the derivative of f(x).

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find the derivative of the function f(x)=(x2+1)^3(3x+4)^4 at x=−1

A:

Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: Consider the following function. 5x, f(x) = XS1 %3D 5x2, x > 1 Find the derivative from the left at…

A: The derivative from the left side of  x=1 is…

Q: The second derivative for the following function at x = 2 f(x) = v2x + is O 1 O 1/4 O 1/2 O 3/4

A: Use the basis concept of integration and derivative than simplify.

Q: Find the given higher-order derivative. F(3)(x) = Vx², f(4)(x) f(4)(x) =

A: Given that, the higher order derivative f(3)(x) = x23 To find the higher order derivative of f(4)(x)…

Q: For the following function f(x)=2e1.5x 1- Obtain the first and the second derivatives for x =3 and…

A:

Q: Find the slope of the line tangent to h(x) = f(x)g(x) at x = 6, given that the line tangent to the…

A: We have to find

Q: Find the derivative with respect to x of 1 f(x) V3x + 9

A:

Q: compute a formula for the nth derivative of f(x)=e2x

A: We have givenWe have to find a formula for nth derivative of f(x)

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

A:

Q: Compute the derivative of the given function. f(x)=−4x^π+4.1x^1.3+π^1.3

A:

Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

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: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: 2. g'(x) where g(x)=x² +7x-5 %3D

A: In this question we need to find a derivative of the given function.

Q: Find the derivative of f(x)=(x+4)e^(5x)

A: We have to find the derivative of f(x) ,where f(x) is given by

Q: Let f(x) = derivative f'(x) equals o. e. Find the value of x for which the second

A: Given that: f(x)=32x2-ex

Q: 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…

A: We need to find relation between f and g.

Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

A:

Q: Consider the following function. f(x) = V36 – x² Find the derivative from the left at x = 6. If it…

A: using the first derivative definition of limit

Q: Compute for the derivative of the function below for x = 1. f(x) = 2xe

A: Solution: dydxx=1=2xex

Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: Given function: gx=4e3x5+2x Differentiate the above function w.r.t 'x' g'x=ddx4e3x5+2x

Q: 1. Find the derivative of the following. f(x)=13x* –7x³+5x²+11x+75 b. S(x)-(x*+2x*+4)(x"-3) 3x -6x+7…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the given higher-order derivative. f(3)(x) = /x5, f(4)(x) f (4)(x) =

A: Given,f3(x) =x56d3f(x)dx3= x56 = z(say)We have to finddzdx= d(d3f(x)dx3)dx = d4f(x)dx4 = f4(x)

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)3 5. h(x) x+5 = x2-9, 6. A(x) = v3x3 +…

A:

Q: [Q2] For the following function Ax)= x² + 2x 1- Obtain the first and the second derivatives for x =3…

A:

Q: Find the derivative of f(x)=(x−2)e^(−3x).

A: The first derivative of the function f(x) = (x−2)e−3x is calculated as follows.

Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

A:

Q: Find the function with the derivative f'(x) 3x = e whose graph passes through the point P| 0,

A:

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 3 5. h(x) x+5 = x2-9, 6. A(x) = v3x³…

A:

Q: Find the derivative of the following function f(x) = 5(x + 47)^2 * %3D O f (x) = 10x + 470 %3D O.f…

A: The given function f(x)=5x+472

Q: Find the approximate value of the function f(x)=√5x−1 at x=1,99.

A: Given Here a = 2. The formula for approximate value is Substitute a = 2 in given function to get…

Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: Find the first derivative for the following function. f(x) = 3/7x² – 2 %3D A. f'(x) = 21x(7x² –…

A: Find the derivative

Q: Compute the derivative of the function f(x) = S7+3x²' at the point 4, using the definition. Ex. 2.…

A: Derivative.

Q: 8.) f(x) = v5x6 – 12 10.) f(x) = (x - 4x- 7)

A:

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.