Finding Derivative Values In Exercises 79-84, find the value of (f ° g)' at the given value of x. 79. f(u) = u + 1, u = g(x) = Vx, x = 1

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. y=\sqrt[3]{6 x^{2}+1}

A: y=3(6x2+1)

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 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 7–26, usethe rules of differentiation to find the derivative ofthe…

A: y=x7

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

A: Solution:Giveng(x)=sinx exFormula:(uv)'=uv'+vu'(sin x)'=cos xex'=ex

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

A: Given: 9. 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 97–102, find dydx byimplicit differentiation.97. x2 + y2 = 64

A: x2+y2=64

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

A: Differentiation is a method that used to find the rate of change of a function . Let one variable be…

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y=\frac{1}{\sqrt{3…

A: Given: y=13x+5

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: 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: 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: Analyzing critical points Use the Second Derivative Test to classify the critical points of ƒ(x, y)…

A: First, We find the critical points for  : f(x,y)=xy(x-2)(y+3)  .......(1) Derivative of equation…

Q: funchoN fo -2x3 + lox218X nd the derivativef"x)=

A: Given f(x) = 2x3 + 6x2 - 18x - 54f'(x) = 6x2 + 12x - 18

Q: Puestion 4. Using the definition of the derivative, show that f(x) = ifferentiable at x = -3. |2x+6|…

A: we have to show

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

A: Tangent line is horizontal if the slope of the function is zero, and the line is horizontal with…

Q: calculus:

A: we have to find the derivative of the given function f(x). f(x)=7log5(x5-9x)

Q: QI) Find the directional derivative Duf (x, y) of the function f(x, y) = evx2+y² at (2,0) in the…

A:

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

A: Here, the function is f(x)=ex cos x. According to the power rule of differentiation,…

Q: Calculate the derivatives of all orders:  f '(x), f ''(x), f '''(x), f (4)(x),   , f (n)(x),    f(x)…

A:

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

A:

Q: Can I get step by step helpn with this problem?

A: Given:

Q: Finding a Derivative In Exercises 5–26, finddydx by implicit differentiation. 5. x2 + y2 = 9

A: Implicit differentiation:       Implicit differentiation is the procedure of differentiating an…

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

A: Given function: y=x12

Q: total derivative of the function f(x, y

A:

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: Derivative Calculations In Exercises 1–12, find the first and second derivatives.

A: We use the power rule to find the first derivative. Power rule: d/dx(x^n)= n*x^(n-1)

Q: In Exercises 33–46, find the derivative.

A: To find derivative of y=ecos-1x. Chain rule of derivative states that: ddxfgx=f'gx·g'x…

Q: Can I get step by step helpn with this problem?

A:

Q: Estimate the slope of the tangent line of the function f(x)=3ex at the point x=e. slope of the…

A: Slope of the tangent line is given bythe first derivative of curve at given point.

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

A:

Q: Calculate the derivatives of all orders:  f '(x), f ''(x), f '''(x), f (4)(x),   , f (n)(x),    f(x)…

A:

Q: derivative of  f(x) = x csc(x) - 4cos(x)

A:

Q: Analyzing critical points Use the Second Derivative Test to classify the critical points of ƒ(x, y)…

A: Given : f(x,y)=x2+2y2-4x+4y+6…

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

A: remember this:…

Q: Finding a Derivative In Exercises 81–86, find F'(x). sin x 83. F(x) = Vi dt 84. F(x) = %3D 2r 85.…

A:

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: Consider the given function as y=cos3x+3cosx+79

Q: f(x) dt f' (x) = %D

A: Detailed solution is given below.