In the six exercises below, assume that the function has an inverse. Without solving for the inverse, find the values of the inverse function and its derivative at x_a, and graph the inverse function. f(x) = x³ + 4xr – 1, (a) a = -1, (b) a = 4

Q: In the given equation , find the second derivative of the function :-   f (x) = 5(2 - 7x)4

A: In the given equation , find the second derivative of the function :- f (x) = 5(2 - 7x)4

Q: A1) Using the definition of derivative, find the derivative of f(x) = x² + 7x + 7.

A:

Q: Write a derivative formula for the function. f(x) = 8x√(7x+2) +91

A: Given,

Q: Give 3 expressions that have the following as a derivative. x) +x²

A:

Q: Find the derivative of the function.(x2 + 9)(x3 + 6)/ x2 + 3

A: Consider the function

Q: Use logarithmic differentiation to find the derivative of f(x) = x(x2 − 8)2/x-9

A:

Q: Using the definition, find the derivative of the simplest quadratic function y=x2.

A:

Q: Using the definition of derivative, find the derivative of f(x) = x² + 3x + 3.

A: Solution:

Q: Find the equation for f-1, the inverse functions, of f(x) = 5x + 2. Verify that your equation is…

A: Solve as below

Q: A1) Using the definition of derivative, find the derivative of f(x) = x2 + 8x + 8.

A:

Q: Using the definition of derivative, find the derivative of f(x) = x² + 4x + 4.

A:

Q: Consider the following function. In each case, without finding the inverse, evaluate the derivative…

A: The function is f(x)=x And given point is (2, 4)

Q: Write a derivative formula for the function. f(x) = 2x 5x + 6 + 91 f'(x) =

A: To write the derivative formula of the given function.

Q: How do you find the derivative of an inverse trig function?

A: Note that, there are six trigonometric functions which also have inverses. There are general formula…

Q: When it comes to finding the inverse of a function, does step 3, solving for y, always involve the…

A: i.e. Step 1 To find the inverse of f(x)=-13x+1 Place y in for the f(x) ⇒y=-13x+1 Step 2 Interchange…

Q: Write an equation for the inverse function for f(x) Зх — 1.

A: Consider the provided equation,  fx=3x-1 Find the inverse of the equation. We can write as, y=3x-1…

Q: Write the formula for the derivative of the function -4 g(x) x2 = g '(x)

A: Formula:

Q: Using the definition of derivative, find the derivative of f(x) = x² + 6x + 6.

A: Here we can find the derivative using definition as below.

Q: Given f(x)=−5tanx, fill in the blank with the derivative of the function.

A: Given the function  f(x) = -5tanx  we need to find it's derivative   As we know that the derivative…

Q: Write the formula for the derivative of the function. f(x) = 11x4 + 15x3 + 9

A: Given query is to find the derivative of the function.

Q: Using the definition of derivative, find the derivative of f(x) = x² + 3.

A: As per our guidelines, we are supposed to answer?️ only one question.   B2(a). Find the derivative…

Q: What is the inverse to function #5 and how do I solve it?

A: We have to use properties of inverse function.

Q: Without finding the inverse, evaluate the derivative of the inverse at the given point.  f(x) =…

A:

Q: How do you solve an inverse function?  f(x)= 2x+3

A: To find inverse of the function f(x) follow the following steps given belowReplace f(x) with y.Then…

Q: How do I find the inverse function of f(x) = 1/x+4?

A: Given function,  Let y = f(x)

Q: Consider the following function. In each case, without finding the inverse, evaluate the derivative…

A: Given function is fx=12x+8. Differentiating the given value with respect to x, f'x=12·1+0=12 Since,…

Q: Consider the following function. In each case, without finding the inverse, evaluate the derivative…

A: Given function is fx=x2-2x-3. Differentiating the given with respect to x, f'x=ddxx2-2x-3=2x-2 Now,…

Q: Find the second derivative of h(x)=x2+3x-3 Simplify your answer, if possible.

A: Our objective is to find the second derivative of h(x)=x2+3x-3.

Q: Find a formula for the derivative of the function 2x2 – 3

A:

Q: Using the definition of derivative, find the derivative of f(x) = 22 + 6x + 6.

A:

Q: What is the equation of the inverse for this function?

A: we have to find the inverse of the function f(x)=log2(9x)

Q: Using the definition of derivative, find the derivative of f(x)= x² +3.

A: (As per bartleby guidelines, for multiple questions asked, only first one will be solved. Please…

Q: Find the inverse of the function f(x) = – 5x² . f-'(x) = The domain of ƒ-' is

A: Solution:- let f(x)=y

Q: What procedure can you sometimes use to express the inverse of a function of x as a function of x?

A: Consider f(x) to be a function of x.

Q: Given f(x) = x, use the Derivative Rule for Inverse Functions to determine (f-')'(-243). Write the…

A:

Q: the

A:

Q: Write the formula for the derivative of the function. f(x) 7x-0.7 f'(x) =

A: To comute the derivative of the given function y=f(x)

Q: find the derivative  f(x)=x2(x3-1)

A: Apply the product rule and obtain the derivative of the given function.

Q: Find the derivative f(x) = 1x1= 2-x -X f'(x) = ? ×20 x <o

A: We have the function, f(x)=x=xx≥0-xx&lt;0 We need to calculate f'(x).

Q: B2(a): Using the definition of derivative, find the derivative of f(x) = x² + 7.

A:

Q: A1) Using the definition of derivative, find the derivative of f(x) = x² + 2x + 2.

A: I have appended the formula used in the solution part.

Q: Find the derivative of the inverse of the following function. Express the result with x as the…

A: Consider the given function, fx=12x-16 so, it can be written as, y=12x-16 now, replace x with y,…

Q: Write the formula for the derivative of the function f(x) 29x7 f'(x) =

A: The given functions are

Q: Given f (x) = x³, use the Derivative Rule for Inverse Functions to determine (f-1)'(216). Write the…

A: In this question we have to find the value of the inverse derivative of the function at the given…

Q: Find an equation for the inverse function. 51) f(x8*-3

A: Consider the function f(x)=8x-3.

Q: Given f(x)=e²x, determine the value of f(¹¹) (11th derivative)

A: Given  f(x) = e2x. We have to determine the value of  f11.

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: f'x=-2x8-x2    passes through the point2,2x,y=2,2Indefinite integral:∫f'x dx=Fx+C

Q: Find the second derivative of the function f(x) = 5(2 − 7x)4

A: Find the first derivative as shown below: f'x=ddx52-7x4        =42-7x3ddx2-7x        =5· 42-7x3-7…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.