Let f(x)=5.9x^2-4.5x. Find the equation of the secant line on the graph f(x) between x1=6 and x2=12. write your answer in mx+b format.

Q: Solve for the derivative of the function using chain rule. 4. f(x)= (x3+4)5/ 3x4-2

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Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

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Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: Find an eqaution of the line tangent to the graph f(x) = 3x2 - 5x at the point (1,-2).

A: fx=3x2-5x Slope of the tangent line is the derivative of the given function at the given point. So…

Q: What is the derivative of y = 3x²tan-1(x)?

A: ddxxn=n xn-1ddxtan-1x=11+x2 One have to use product rule here, which is ddx(uv)=vddxu+uddxv

Q: What is the maximum slope of a tangent to the function f(x) -x³ + 4x - 2? ==

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Q: Find the third derivative of y = (6x - 1). Show your %3D in negative exponent.

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Q: Find derivative using product or quotient rule

A: f'(x)=((x2)'(x+3)(4x-1)-x2((x+3)(4x-1))')/((x+3)(4x-1))2       (Using quotient rule)…

Q: 5. Find the derivative by using the quotient rule. 3x - 2 (a) 2x +3 V+2 (c)- 3+2x (b) x +1 x+2 (d):

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Q: Find anti derivative of    f(x)= (2x2+1)(3x-2)

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Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: Find the derivatives of the functions in Exercis y = (4x + 3)4(x + 1)-3

A: y=(4x+3)4(x+1)-3

Q: Find the first derivative: y= In V5x3 - 2

A: Given: y=ln5x3-25 We need to evaluate dy/dx. This can be done as follows:

Q: Find the derivative of y=7tan^-1(x-(sqrt(1+x^2)

A: Chain rule:

Q: Find an equation of the line tangent to the graph of ƒ(x) = (2x - 1) (x + 4) at (1, 5).

A: To findEquation of the line tangent to the graph y=(2x-1)(x+4)  at (1,5)⇒y=2x2+7x-4.

Q: Find the derivative of f (x) = (5 – 3x)2. %3D

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Q: The fourth derivative for * 3 points y = x3 - 3x2 + 2 are 6x-6

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Q: Use the second derivative test to find the local extrema for the function. y = 3x5- 25x3 + 60x + 20

A: We can use the application  derivative in order solve the given problem.

Q: Find derivative of y= x(3x-1)5

A: Use the product rule to differentiate the given function with respect to x…

Q: Find the derivatives of the functions in Exercis y = (2x - 5)-1(x2 - 5x)6

A: Given function - y = 2x-5-1x2-5x6y = x2-5x62x-5               ........(1)  Identity to be used -…

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

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

A: The given function y=x2+2x

Q: se the General Power Rule to find the derivative of the f y = 124x2 + 5

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

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

Q: Compute the derivative f(x)= cubed root of x + 3/x5

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Q: Find the derivative of f(x) = (2x^2-x-1)(sqrt of x) %3D

A: A detailed solution is given below.

Q: Use the the derIva tive rule to find derivative of Y= 2x3 -1 X-1 メ 6x -5 X² +1

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Q: Use the definition of derivative to find f(x) = 2-x+2x^2

A: Given,          fx=2-x+2x2

Q: FInd the derivative of  y=(3x-2)2(5-x5)4

A: Assume u=(3x-2)2 and v=(5-x5)4 Differentiate the function u with respect to x. Assume p=3x-2…

Q: 7. y = Vx + 2

A: Using Delta method differentiate y. And using rationalising.  Follow step 2nd  .

Q: Find the equation of the line tangent to the graph f(x)= (lnx)5 at x=5

A: First find slope then use equation of tangent tangent line

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

A: To sketch the graph

Q: Use definition to find the derivative of the function f(x)= 2x-3x2 at x = 3 %3D

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

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

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: Find the derivative of the function.

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Q: Find the derivative of the function without using the Quotient Rule. 4x -27 y' = ( 4x10)

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Q: Find the first derivative y = (3x-2)/ (2x-1)1/2        Use the quotient rule

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Q: Find the derivative of the function. f(x) = 2x In 2x %3D

A: Given, f(x)=2xln2x To find the derivative of f(x).

Q: 2. 2x +1 %3D 2.

A: We have to find the derivative of y

Q: Find the derivative of the function y = sech 5x2

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Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Find the local extremes of f (x) = x³ +2x+ using the first derivative test.

A: Given,         The local extremes of fx=x3+34x4 using the first derivative test.

Q: Find the derivative. y = 5x(2 – x³)* %3D

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Q: with positive exponents only

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Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2

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: Find the higher order derivative. f"(x) = 4x2 + 9x – 16 - f(5)(x) = %3D

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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: