71. Let f(x) and g(x) 1 %3D a) Compute f'(x). b) Compute g'(x). c) What can you conclude about the graphs of f and g on the basis of your results from parts (a) and (b)?

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A: Hence, sinh x is increasing for all x.

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A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

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A: According to the question; f(x)=ex+x                                                     ; x=2step…

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A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: Find Taylor s Sen'ey fer ci) f() = Sin (x) about x= | f (x) = los (x) about f(x) = about x=1

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

Q: Can you help me with this problem step by step?

A: The given equation,

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A: We will find the derivative of y with respect to x as following.

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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A: To find the extreme points.

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Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

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Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

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A: Find gradient and its magnitude then solve

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Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x…

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Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

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Q: 3. Use the forward-difference formula to approximate the derivative of f (x)=sin(In x) at x, = 2.5…

A: The derivative of the function can be calculated using the difference method. The formula for the…

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: Compute forward and backward difference approximations of O(h) and O(h2), and central difference…

A: Numerical differentiation includes three different types: forward difference, backward difference,…

Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

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Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

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Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

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Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

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Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

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Q: Q Find the derivative us ing the de fini tion 2. O fcx) Fcx) x+2X %3D

A: Derivative of the function using definition

Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

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Q: Find the values of x on [0, 2 ) π where the tangent line of f x( ) be horizontal. y=e^-x (cosx)

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Q: What is the derivative of y = 10sin Sx 5 In 10 cos x 10sin Sx 5 In10 (10sin Sx ) A. В. C. 5 cos x In…

A: Given: y=10sin 5x To Find: The derivative of the given function.