Use the graph of y = f(x) to sketch the graph of f'(x). 10+

Q: Find the first derivative of y=x arcsin x + √1-x²

A: y=x arcsinx+1-x2

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the derivative of the function f(x) = (In x)°.

A: Given that,             f(x) = lnx3 Differentiating with respect to x, we get                  f'(x)…

Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

Q: Find the derivative of f(x) = 2 tan^-1(x) 6^x

A:

Q: Find the Derivative of f(x)= tan(- -3

A: We have to find the derivative of function: fx=tan x3x2-3 We know the formula of derivatives, d tan…

Q: f(x) = Arctan csc² ( 3x

A: Some derivative formulae: ddxtan-1x=11+x2ddxcscx=-cscx cotx Chain rule of derivative:…

Q: -Find the range of the function y = 2 - sin3x

A: Introduction :

Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

A:

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Using the criterion of the first derivative, find the graph of the function: F(x) = 114 (x*) + 4,…

A:

Q: Find the derivative of the function. y- tan-(V-8

A: In this question, we need to calculate the derivative of the given function.

Q: Find the derivative of f(x)=arctan(1/x) and simplify

A:

Q: Find the derivative using the Four-step rule f(x)=x/1-x

A:

Q: Find the nth-order derivative of the function y=x2cosx.

A:

Q: he figure shows the graph of the derivative f' of a function f. yA y= f'(x) -2/

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Find the derivative.

A: Given: To find the derivative of y=2x-3-xx

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

A:

Q: Find the derivatives of the function f(x) from the first principle x*+4

A:

Q: Find the derivative of f(x)= xtan(x)

A:

Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

A:

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: 6. Sketch the graph of y= x2+ by using the properties of the derivative.

A: The given function y=x2+2x

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Find the derivative of the function f(x)= xsinx+x^2e^2-1.

A:

Q: Find the derivatives using the four step rule: f(x) = 1-x2

A: Explanation of the answer is as follows

Q: Find the derivative of the functiony=tan^2(6x)

A: we have to find derivative of f(x)we will use following rules

Q: find the derivative of the function f(x)=x^3+2x at -3

A: find the derivative of the function f(x)

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the…

A:

Q: Find the derivative of the function using chain rule. f(x) = esin?x

A:

Q: Find the first derivative of f (x) = 2* 2*

A:

Q: Help to find the derivative of f(x)=1/3x.

A: The given function is fx=13x

Q: Find the derivative of the function. y= 2^(3-x^2)

A: Given function

Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

Q: f(x) = x' tan (5x)

A: Explanation and solutions is given below....

Q: Draw the function x = 2y-y2 by using the tools of derivatives?

A: The given function isx=2y-y2.

Q: Find the derivative of the function. g(x) = 2(3- Ex)

A:

Q: 5. Sketch the graph of y = x3 + 5x2 + 3x - 4 by using the properties of the derivative.

A: Find f' (x) then we check f(x) increasing Or decreasing.

Q: 5+x f(x) = 3—х

A: Solve the following

Q: 2) Find the derivative of the function f(x) = 3x² by definition

A:

Q: Find the derivative of the function. h(x) = x² arctan(8x)

A:

Q: Find the derivative. f(x) = 4cosx + √x

A: Given function is fx=4cosx+x. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating…

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: 4. Find the 2nd derivative of f (x) = 4-x x)%3)

A: To determine the second derivative of the function given by; f(x)=4-x Differentiate the function…

Q: Sketch the graph of y= x2+2/x by using the properties of the derivative.

A: Given: y=x2+2x=x2+2x⇒y'=1-2x2⇒x2-2=0 ;  ⇒x=±2 are…

Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…

Q: What do you look for when you need to match the graph of a function with the graph of its…

A: Observe the behavior of graph as the value of x increases.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: