1. Use the Product Rule to find for y=(4x'-3x)(2x* +5).

Q: 4. Find the equation of the tangent line to the graph of f(x)= 2x² – In Vx at x = 1.

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Q: 2. Find the slope of the tangent line to the curve y = x3 – 2x + 1 at x = 1.

A: As we know that: The first derivative of the function at a point is equal to the slope of the…

Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: 1. Find the equation of the tangent line to x2- 3xy +y2 = -1 at (2,1).

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

Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

A: The equation of tangent line can be found by using the formula,y-y1=mx-x1Where, m=dydxx1

Q: Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

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Q: 7. If the tangent line to y = f(x) at (-1,3) passes through the point (2,1), find fl-1) and f'(-1).

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Q: 7. Find the dy/dx of * y = In sin 5x

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Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

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Q: 6. Find the equation of the tangent line to x² + 3xy + y² = 5 at the point (1, –4).

A: Given x2+3xy+y2=5       (1,-4)

Q: Find the derivative of y 16 In (In(6x)). (Use symbolic notation and fractions where needed.) dy dx…

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Q: 2. Find the equation of the tangent line to the curve y = In(x'-7) at (2,0).

A: Given :          y=lnx3-7

Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

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Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: 5. Write the equation of the tangent line to the curve of y = e³x + cos(-x) at the point (0,2).

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Q: 4. Find the equation of the tangent line to the function y= In(x* -2) when x=3.

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Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: 2. Find the equation of the line tangent to x* – 3xy+ y³ = 1 when x = 0.

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Q: Calculate the partial derivative using implicit differentiation of e4xy + sin (5xz) + 4y = 0. (Use…

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Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: Find the derivative of cos(3x) O -3sin(3x) O 3sin(3x) O 3cos(3x) O -3cos(3x)

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Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

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

Q: If –5 + y³ = xy² – x and it is known that find all coordinate -2xy+3y2 > 2 and the line tangent to…

A: consider the curve         -5+y3=xy2-x  ⋯⋯⋯⋯⋯ (1)  and             dydx=y2-1-2xy+3y2  To find all…

Q: Find the slope of the tangent line on the curve y = x3 - 2x2 – x at x = -2. -6 O -19 O 19 O 6

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

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Q: y = In (5x- 6x • 6), Hthe derivative, y' 2. 1S

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Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: 2 If 3x? + 4x + xy = 1 and y(1) = - 6, find y'(1) by implicit differentiation.

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Q: 2. Find the equation of the line tangent to x³ – 3xy + y = 1 when x

A: Given:               x3-3xy+y3=1,     x=0 at x = 0               0-30y+y3=1y3=1y=1 The slope of the…

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: Find y" by implicit differentiation. 4x3 + 3y3 = 4 %3D

A: Given: 4x3+3y3 = 4 To find: The value of y'' by Implicit differentiation.

Q: 22. Find OY if y2 - 4xy + x² = 10. dx

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Q: 3. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF 5x + 2xy + 4y² = 25 AT THE POINT (1,2).

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: Find the slope of the line tangent to the curve x^3 - 3xy + 4x = 2 at x=1.

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Q: Find the approximate root of y = 2x2 + 4x – 6 when x = 0.01 using differentials. -

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Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

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Q: Find y ' by implicit differentiation for 4x² y7 – 2x = x5 + 4y3 . %3D

A: We have to find y' by implicit differentiation of : 4x2y7 - 2x = x5 + 4y3

Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: 3. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF 5x + 2xy + 4y² = = 25 AT THE POINT (1,2).

A: Given: 5x+2xy+4y2=25

Q: Find y't yu 4=In(sec 9x +tangx)

A:

Q: 7-The tangent of the curve x^2+y^2- 2XY3D0 at the point (1,1), is *

A: Given,           The curve is x2+y2-2xy=0 at the point 1,1.

Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.

Q: 4) Determine the equation of the tangent line to y=3x -5x² +10 at x= 1

A: The given equation is; y = 3x4 - 5x2 + 10  at x = 1