Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the tangent line horizontal?

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Using Leibnitz theorem, the nth derivative of xy, is

A: We have to find nth derivative of xy1 using Leibnitz theorem.

Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

A:

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: Find the Equation of tangent line of the function f(x) = 1 + csc(x) – /cos(x) 2n 4+V3 23 At the…

A: Consider the provided function, fx=1+cscx-cosx and the given point 2π3,4+323. Find the equation of…

Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

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Q: What is the derivative of f (x) = cosh(x) + sinh(x)?

A: Given that f(x)=cosh(x)+sinh(x) find the derivative of f(x)

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 transcendental function y=e^x-cotx

A: Given,             y=ex-cotx

Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: Find fifth order derivative of the function f(x) = x*Sin (2x +1) by using Leibnitz theorem.

A:

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 of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

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Q: tion of the tangent line to f(x) = 4 %3D

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Q: find the derivative of y with respect to the appropriatevariable. y = sinh-1 √x

A: Find the derivative of y with respect to the appropriate variable.

Q: Using limit definition of derivative, prove d/dx e^x=e^x

A: We using limit definition

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: 2. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

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Q: fcx)= Y文 メ ー^

A: Local extrema

Q: 4. Use implicit differentiation to find an equation for the tangent line to the graph of sin(x +y) =…

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Q: Find derivative of f(x) = ln(5x + 2) The slope (as fraction) of the tangent line at x=2 is

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Q: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…

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Q: 2. Use the implicit differentiation to find an equation of the tangent line to the curve at the…

A: Given curve ,yesinx=xcosyNow using implicit differentiation , we…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

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

A: Given equation of curve is (x2+y2-y)2=x2+y2 Differentiate both sides with respect to x.…

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: find the derivative of y with respect to the appropriatevariable. y = (x2 + 1) sech (ln x)

A: Given: y=x2+1sechlnx

Q: 3. Use implicit differentiation to find an equation of the tangent line to the curve 2(x + y = 25(x…

A: Explanation of the answer is as follows

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Using central difference, find the second-order derivative of y=x²cosx at x=9, h=0.1

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Q: Find the derivative of the function using chain rule. f(x) = esin?x

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+V3 2V3 At the…

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Q: Find the derivative of the function g(x) = (arctan x)³, first showing how to get the formula for -…

A: Consider the function  g(x)=tan−1x3

Q: 4. Use implicit differentiation to find an equation of the tangent and normal line at the given…

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

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Q: nd derivative of f(x) = x In(x)

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

Q: Find the equation of the tangent line to the curve given by f(x) = x2 ln x at the point  (1, 0)

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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: Find all x values on the graph of f(x) = - 3 sin x cos x where the tangent line is horizontal.

A:

Q: The second derivative of an anti-derivative of a differentiable function F R-R is: O possibly…

A: The second derivative of an anti-derivative of a differentiable function f:R→R is

Q: 8) Using your derivative from the previous question, determine the equation of the tangent line at…

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Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)

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Q: Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h =…

A: Given  f(x) = sinxx we have to obtained the first derivative of f(x) by using  Richardson's…

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

A: