Determining Differentiability In Exercises85–88, find the derivatives from the left and fromthe right at x = 1 (if they exist). Is the functiondifferentiable at x =1? \text { 8. } f(x)=(1-x)^{2 / 3}

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y = 5(2 − x3)4

A: We have to find the derivative using the chain rule of differentiation . According to the chain rule…

Q: Using the Product Rule In Exercises 5–10,use the Product Rule to find the derivative of thefunction…

A: According to the product rule of differentiation , The differentiation of the functions of the form…

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A:

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function.…

A:

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y=\sqrt[3]{6 x^{2}+1}

A: y=3(6x2+1)

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function.g(x) = [2 + (x2 + 1)4]3

A: The given function is, 2+x2+143. The objective is to find the derivative of the function. Power…

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: Given, y=12ex-3sinx To Find: dydx

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: The given function is: y=t2-3t+1 Find the derivative of the function.

Q: Finding Derivatives Implicitly andExplicitly In Exercises 27–30, (a) find twoexplicit functions by…

A: Explicit differentiation is the process of differentiating an explicit function. the explicit…

Q: Finding a Derivative In Exercises 41–58, findthe derivative of the function. \text { 44. } f(x)=8…

A: To find: The derivative of fx=8x+3x2. Concept used: Sum or difference rule of derivative:…

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: To find the derivative of equation y=x2-12cosx, use following rules of differentiation. Power of…

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: y=x7

Q: Derivatives of Functions Find the derivatives of the functions in Exercises 1-40. 34. y = 4xVx + Vĩ

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. g(x)=3(4-9 x)^{5 / 6}

A: Given : The function is g(x) = 34 - 9x56 .

Q: In Exercises 13–18, calculate the derivative in two ways. First use the Product or Quotient Rule;…

A:

Q: Evaluating a Second Derivative In Exercises 129–132,evaluate the second derivative of the function…

A: Derivative determines the change of one variable with respect to another variable. When the…

Q: Slope of a Tangent Line In Exercises 97–100, find theslope of the tangent line to the graph of the…

A: y=e-3x

Q: Using the Quotient Rule In Exercises 11–16,use the Quotient Rule to find the derivative of…

A: Given that, g(x) = sin xex

Q: Logarithmic differentiation Use logarithmic differentiation to evaluate f 1x2.

A: Given, f(x)=xln(x)

Q: Finding a Derivative In Exercises 31-44, find the derivative of the function. sin x 36. у %3D

A:

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. f(t)=(9 t+2)^{2 / 3}

A: Given function - f(t) = 9t+223          Differentiating on both sides with respect to 't' - f'(t) =…

Q: Finding a Second Derivative In Exercises59–62, find d2ydx2 implicitly in terms of x and y. 59. x2y…

A: Implicit functions in 2 variables are obtained when both the variables are used to define the…

Q: Horizontal Tangent Line In Exercises 63–70,determine the point(s) (if any) at which the graphof the…

A: Consider the function, y=x4-2x2+3 A horizontal tangent line has a slope of zero; therefore we need…

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y=\frac{1}{x-2}

A: The rate of change in the value of the dependent variable with respect to the change in the value of…

Q: Finding an Equation of a Tangent Line In Exercises43–46, find an equation of the tangent line to the…

A: Given function is fx=x+2x2+5. To find the equation of the tangent line to the graph of f at point…

Q: Finding a Second Derivative In Exercises 89–92, find thesecond derivative of the function.89. y =…

A: given,         y=8x+53

Q: Approximating Function Values In Exercises 43-46, use differentials to approximate the value of the…

A:

Q: Finding a Second Derivative In Exercises 45-50, find d?y/dx² implicitly in terms of x and y. 45. x2…

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Q: In Exercises 93–96, use the table of values to calculate the derivative of the function at the given…

A: Given: y=fgx for finding derivative of given function, we differentiate given function so,…

Q: Slopes and Tangent Lines In Exercises 13–16, differentiate the functions and find the slope of the…

A: Given,

Q: Sketching y from Graphs of y' and y" Each of Exercises 81-84 shows the graphs of the first and…

A: 81) It is known that the graph of the function is increasing on I if for f'x≥0 for all x∈I The graph…

Q: Finding a Derivative In Exercises 41–58, findthe derivative of the function. \text { 46. }…

A: Given function is: hx=4x3+2x+5x We have to find the derivative of h(x). We will apply the quotient…

Q: Finding a Derivative In Exercises 41–58, findthe derivative of the function. \text { 48. }…

A: 48. h(s)=s5+2s+6s1/3   ddss5+2s+6s13Apply the Quotient Rule:  fg'=f…

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: Given function: y=x12

Q: Using the Alternative Form of theDerivative In Exercises 69–76, use thealternative form of the…

A: Given function is gx=x2-x. To find derivative at c=1 using alternative form of derivative. Solution:…

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. h(s)=-2 \sqrt{5…

A: Find the derivative of the function .        h(s)=-25s2+3

Q: Finding an Equation of a Tangent Line In Exercises49–52, use implicit differentiation to find an…

A:

Q: Finding a Derivative In Exercises 7–26, usethe rules of differentiation to find the derivative ofthe…

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Horizontal Tangent Line In Exercises 63–70,determine the point(s) (if any) at which the graphof the…

A: given y=x+4exTangent of the given functiony'=ddxx+4ex=1+4exnow for the tangent line to be horizotal…

Q: Applying the First Derivative Test In Exercises 59-66, consider the function on the interval (0,…

A: Given query is to find the interval where function is increasing or decreasing.

Q: 60. Y 3r-5 cost mx) "

A:

Q: Finding an Equation of a Tangent Line In Exercises 85-90, find an equation of the tangent line to…

A:

Q: Evaluating a Derivative In Exercises 65–72, find and evaluate the derivative of the function at the…

A: remember this:…

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: