Find derivatives of f(x) = {x+- 1 and find the line tangent to it when x = 1

Q: Find the derivative of the function.

A: Given: To find: Derivative

Q: use the definition of derivative to find the equation of the tangent line to the graph of f(x) = x2…

A: To find the equation of tangent line at the given point.

Q: Use the definition of a derivative to find the equation of the tangent line at the given point.…

A: The equation of the tangent line is  y-7x+2=0

Q: Find the derivative of y with respect to x if y = (11x2 - 22x+ 22) ex.

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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: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

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Q: y = In

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Q: Find the derivative of f(x) = 1 at x = 3

A: The given function is: fx=1x Using the formula of derivative i.e., ddxxn=nxn-1

Q: Find the derivative of the function

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

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Q: Find the derivative of each function at the specified value of x.

A: We have to find the derivative of the function at the given value of x: gx=ex sinπx, when x=0. We…

Q: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

Q: find the equation of the tangent lines using implicit differentiation 2xy+x^2=3 at (-1,1) and…

A: Given: Equation of the curve,       To determine: Equation of the tangent line at (i) (-1, 1) (ii)…

Q: Compute the derivative using derivative rules.

A: Explanation Given that,  y=(kx+b)-13   Differentiate with respect to x both the sides…

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Find first the derivative as shown below: f'x=ddx-5-x2        =125-x2ddx5-x2       =-125-x2-2x…

Q: Find the derivative of the function 3 tan (x- 2 1 x y

A: Given:

Q: Find the derivative of the function.

A: Given: g(x)=arcsin(3x)x

Q: y = x*(1 – In x4)

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Q: Find the derivative of the function. x + 6 X-6 y' = y = In

A: I have appended the formula used in the solution part of the question.

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

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: 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: (3x+4` x² +5, y = tan

A: We know that d(tanx)dx = sec2(x) Now we will apply chain rule , Here we have    y = tan3x+4x2 +…

Q: find the equation of the tangent line to the graph of f(x) = x^3 + 3x^2 at the point (1, 4) without…

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Q: Find the derivative of the function f(x.y) = tan -1 y at the point (4, - 4) in the direction in…

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Q: Find the derivative of y with respect to x. y= csc^-1 (x^2+1) , x>0

A: Given ,

Q: Find the derivative of y with respect to x using implicit differentiation in the equation *'y =…

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Q: Find the derivative of y with respect to x.

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Q: In 2x y = - cos x

A: ddxln 2xcos x= ddxln 2x . cos x - ln 2x.ddxcos xcos2 x= 12x. 2. cos x - ln 2x.(-sin x)cos2x= cos xx…

Q: Find the derivative of the function (slope of the tangent) using the definition at the point Xo=9…

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Q: Can you help me step by step?

A: To differentiate the given expression y=f(x)

Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

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Q: y = cof'/ x2-1 x²+

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Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec-1

A: Let, z=(2x+3)/5   We differentiate using the chain rule

Q: Find the derivative of the function

A: We have to find the derivatives of the function: y=x tan-12x-14ln1+4x2 If two functions are in…

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 derivative of f(x)=x2-3x. Use the result to find the slope of the tangent line to the curve…

A: Given: fx=x2-3x To Find: The derivative of the given function and the slope of the tangent line at…

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 the function f(x y) = tan-1Y at the point (5, -5) in the direction in which…

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Q: Find the derivative of y with respect to x y = csc^(-1)(x^6 + 1), x> 0

A: Find the derivative of the given function.

Q: The tangent line to f(x) = x² at x = –3.

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Q: Find the derivative of the function. g(x) = 2(3- Ex)

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Q: Find the derivative using the definition 1- y = vx -1

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Q: Find the derivative of y with respect to x. 58)y tan (In 2x)

A: Firstly, we use the result that  derivative of inverse of tan of x is 1/1+x^2

Q: Find the derivative of the function. y [x + (x + sin²(x))-1*

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Q: Use the definition of derivative to find the tangent and normal equations of f (x) = (x – 3)2 %3D

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Q: Find the second derivative of g(x) = secx.

A: Given : gx = sec2x

Q: Use implicit differentiation to find an equation of the tangent line to the curve 2-x +x-y+ 2·y² = 5…

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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.

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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: