Let f(x) = x'. Find the slope of the line through the points on the curve y = f(x) where x = -2 and x = 3.

Q: Use the Chain Rule to find the derivative. y = sec 1/X

A: Differentiate: y=sec 1x. Apply chain rule: dydx=dydu·dudx Let u=1x dydx=dsec 1xd1x·d1xdx

Q: What is the slope of the line tangent line to the curve x²y = y2 – 6x when x=2?

A: The given curve is x2y=y2-6x. Substitute x=2 in the above equation and obtain that,…

Q: Find y'(x) from y(z) using the definition of a derivative.

A: according to the problem, we have

Q: Find the 4th-order derivative of the function y=xsinhx.

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Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

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Q: Use the Chain Rule to find the derivative. y = sin(x2)

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Q: Find the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

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Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

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Q: Find the slope of the line tangent to the graph of f(x) = xe* at x = 0. %3D

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Q: Find the derivative of the function. y = 9Vx y' = %3D

A: Our Aim is to find the derivative of y=9x -(i)

Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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Q: Find the derivative of y with respect to x if y = (7x - 14x+ 14) eX. %3D dx

A:

Q: Find an equation of the form y = f(r) for a curve with z-intercept 2 whose tangent line at any point…

A: we have to find an equation of the form y=f(x) for a curve with x-intercept 2 whose tangent line at…

Q: What is the slope of the line tangent to the curve x2 + y2 = 1 and parallel to the x=axis ?

A:

Q: Find the derivative of the function f(x,y)=x2+xy+y2   at the point (-5,-4)in the direction in which…

A: Find the derivative of the function f(x,y)=x2+xy+y2   at the point (-5,-4)in the direction in which…

Q: On the same axes, plot the curve y = 1x, the line y = x/8, and the tangent line to y = 1x that is…

A: Given curve is y=x. Let x,y be any point on the curve. Differentiate function with respect to x.…

Q: y = = Vsin va

A:

Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Determine the slope of the line tangent to y = x+1 at x = 1 3x2

A: y = (x+1)/3x2 slope = dy/dx dy/dx = (3x2(1) - 6x(x+1))/9x4 slope at x=1 dy/dx = (3 - 6(2))/9 dy/dx =…

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: Compute Δy Δxfor the interval [4,10], where y= 2x-6   ________   What is the slope of the tangent…

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Q: Compute y / x for the interval [2, 5], where y = 4x - 9. What is the slope of the tangent line at x…

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Q: Find an equation of the tangent to the curve f(x) = /x+ 7 that has slope %3D 4

A:

Q: What is the slope of the line tangent to the graph of g(x)=1/x at x=1?

A: Given that ,         g(x)=1x          find slope of tangent at x=1

Q: Find the derivative of the function. y = 3 tan(x - V1 + x 1 + x2 y' = ||

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Q: Find the derivative of the function. y = xe¬x/ y' = %3D

A: ddxxe-x7

Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

Q: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a

A: given,y=3+4x2-2x3

Q: find the derivative of y=y^x

A:

Q: Find the derivative of the function.

A: Given function is Differentiating with respect to x by using product rule of differentiation, we…

Q: The slope of the tangent to y = 2 – x2 at the point (1,1) is

A:

Q: Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy…

A: Y'= ?

Q: Find the derivative of by using the product rule. * y = (1+ væ³) (x-3 – 2x)

A: To find the derivative of y=1+x3x-3-2x3 using product rule. Solution: Product rule of derivative…

Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

A:

Q: Find the x-coordinate of the point/s on the curve y = 2x – 3x² – 12x + 20 where the tangent line is…

A: The slope of the tangent line to the curve at point P(x,y) is given by,…

Q: y^2 = x^2 +xy

A: Differentiating both sides of the equation.

Q: What is the first-order derivative of y = x^y?

A:

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Find the derivative of the function. y = 3x 8 * - 12x - dy dx II

A: Explanation of the answer is as follows

Q: The slope of the tangent to the curve yx + y²x² -6 at (2,1) is

A:

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

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: Find the gradient of the curve . Y=4x^2 at x=3

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Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

A:

Q: 3. y = Vx*

A:

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: The slope of the line through the distinct points (x1, y1) and (x2, y2) can be interpreted as the…

A: The slope of the line through the distinct points (x1, y1) and (x2, y2) is defined as…

Q: Find the derivative of the function. 7. y%3D Vx +2 y'

A:

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative