Use the fact that derivative of a function at a point is the slope of the tangent line to the graph at that point to estimate a) f'(0) b) f'(1), c) f'(2), d)f'(3)

Q: 2. Find the third order derivative of y = In(secx + tan x). a. secx b. secx tan x c. - sec(x) + 2…

A: Explanation of the answer is as follows

Q: y3D(i+sinx)(I-sinl)!

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Q: The instantaneous velocity of a particle is defined as the derivative of some functions. Select one:…

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Q: Use forward, backward and central difference to estimate the first derivative of f (x) = In at x =…

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Find the derivative of the function f(x.y) = tan -1y at the point (- 9,9) in the direction in which…

A: To find the derivative of a function at a point (-9, 9) in the direction in which the function…

Q: find the derivative of the transcendental function y=e^x-cotx

A: Given,             y=ex-cotx

Q: Find the slope of the tangent line to the curve y- x + 4=0 at the points (8, 2) and (8, -2) in two…

A: We will find out the required solution.

Q: Compute the derivative using derivative rules that have been introduced so far y = √(9 +x + sinx)

A: We have to compute derivative of the function: y=9+x+sin x We know the formula of derivatives,…

Q: Compute the derivative of the function y = 7 sin¬'(x) at the point x = (Use symbolic notation and…

A: A detailed solution is given below

Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e". %3D Equation:

A: To find the equation of the tangent line to the graph of: y=f(x)=ln(-x) at x=x0=-e4 The equation of…

Q: Find the derivative. Simplify where possible.  f(x)= ex cosh x

A: Given function is

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 5s

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Q: Estimate the slope of the tangent line at the point x = 3, for f(x) = In(x). (Use decimal notation.…

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Q: What is the derivative of f(x)=3cos(x)+2sin(x) at the point x=−π

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Q: Choose (a) or (b). The derivative at a point does not exist if the tangent line at that point is (…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Find the equation of the tangent line to the curve at the given point using implicit…

A: To determine the equation of tangent line to the given curve at point (1, 0).

Q: %3D

A: Solving

Q: Find the derivative using the product rule. y = eX In x

A: y=exlnx

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of…

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: What is the derivative of f(x) g(x) in terms of f and g? Compute the derivative of -sin(x) · 2x=1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Estimate the slope of the tangent line to f(x) = tan (x) at the point x = 4 (Use decimal notation.…

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Q: Compute the derivative using derivative rules. y = cos(te- 2t)

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Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: Find the slope of the curve y = tan-!x at a1, b without calcu- 4 lating the derivative of tan-x.

A: Given y=tan-1x

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: Compute the derivative of the function y = 8 sin-(x) at the point x = (Use symbolic notation and…

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Q: show that the function is derivable and that the derivative is continuous.

A: The objective is to show that the given function is derivable and the derivative is continuous.…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Use implicit differentiation to find the slope of the tangent line to the curve defined by 2xy9+xy =…

A: We have to find slope of tangent line using implicit differentiation of the curve 2xy9+xy=6 at the…

Q: Find the equation of the tangent line to the curve at the given point using implicit…

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Q: Find the derivative of the algebraic functions f(x) = x (1-) x+3, : g(x) = x + cotx

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Q: Choose (a) or (b). The derivative does not exist if the tangent line is: (a) horizontal (b)…

A: The derivative at a point is equal to the slope of tangent line to the curve at that point. Now for…

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: Find the derivative of f(x) = sec(tan(x) + cot(x))

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Q: -3 at the point (9,-1) using only the limit 3. Find the exact equation of the tangent line to the…

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Q: Find the derivative of y= sin cos (tan ax)

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Q: f(x)= sinx/cos x+1

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Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

Q: What is the slope of the tangent line at (0,3) to the function f(x) = -sinx+3

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Q: Find the derivative of F(x) = tan (5x + 7), by first principle of differentiation

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Q: y = cos /sin(tan Tx) %3D

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Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A: