What is the equation for a linear function with a vertical stretch/compression by 2/5. BE SURE TO USE f(x)=

Q: Differentiate implicity to find the slope of the following curve at (0,3) x^3+yx^2+x^2-3y^2=0

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Q: y D. E.

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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 y = f(x) x2 +1

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Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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Q: What is the derivative of y = V(x? V(a2 – 1) (x + 1) ? -

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

A: Given that,

Q: 2. Given: y = f (x) = (2x-2 + 5x³). What is the slope (gradient) of the first derivative function at…

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

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Q: What is the equation of the tangent line to the function f(x) = a? + 5x at the point (1, 6)?

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Q: Find the nth-order derivative of the function y=(3x2−2x)lnx, x>0.

A: Use the product rule

Q: .The line y + 2x = 0 is tangent to y = F(x). Determine F(x) if F(x) = 4x³ + 2.

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Q: For the function y = 2x2 + 8x + 9, at the point x = 6, find the following. (a) the slope of the…

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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: At what point on the curve x = 6t2 + 5, y = t3 − 1 does the tangent line have slope of 1/2?

A: We can use application of derivative in order to solve the given problem.

Q: For the functiony = 8x2 + 6x + 5,at the pointx = 8,find the following.(a) the slope of the tangent…

A: Given a function y = 8x2+6x+5.For any funtion f(x) the slope of the tangent at point x=a is…

Q: Find the third derivative of the function: Y = =+ VX3 %3D

A: To find the third derivative of the function: y=1x+x3

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

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Q: What is the slope of the tangent line that touches the graph of In y + e2z-1 = 3y – 4x at the point…

A: Given that: lny+e2x-1=y-4x

Q: Find the equation of the line tangent to the graph of f(x)=(lnx)^2 at x=3.

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Q: Give two different interpretations of the derivative of the function y = f(x) at x = a.

A: If f(x) represents a quantity at any x then the derivative f′(a) represents the instantaneous rate…

Q: 1. What is the instantaneous slope of y = 5 at x = 5?

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Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: Evaluate the derivative of the function y = 2tan ",²+In (e +e).

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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: What is the instantaneous slope of y == at z = 5?

A: for the instantaneous  slope for a function f(x) at x=a we have to find f'(x) and then put x=a in…

Q: A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the…

A: Let the point of contact is (h,ln(h)) We find the slope of the tangent using dy/dx

Q: if the instantaneous rate of change of f(x) at (3,-9) is 5, write the equation of the line tangent…

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Q: Find the derivative of the function y=(x−1)(x−2)(x−3) at x=0.

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Q: Find the derivative of the linear fractional function y=ax+bcx+d.

A: We have to find the derivative of    y=ax+bcx+d ddxy=ddxax+bcx+dWe have to apply division rule…

Q: f y=x^2(e^x)

A: Derivative: ddx(u.v)=u.dvdx+v.dudxy=x2(ex)Here u=x2,v=ex

Q: Find the given flx), + 2x derivative of function. %3D a+x

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Q: At what point on the curve x = 9t2 + 3, y = t3 – 2 does the tangent line have slope ? (x, y) =

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Q: find the equation of the line tangent to the graph of y=3ln⁡(x) at x=3. Tangent Line:…

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Q: Find the equation of the line tangent to the graph f(x) = – at the point (4,1).

A: Given:            fx=4x To find the slope of the tangent line, find the value of the derivative of…

Q: Find the equation of the line tangent to the graph f(x)= (lnx)5 at x=5

A: First find slope then use equation of tangent tangent line

Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: For the function y = 2x2 + 7x + 9, at the point x = 7, find the following. (a) the slope of the…

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Q: Find the average rate of change and the equation of the secant line for 2x f (x) = from -1 to 3. x²…

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Q: Solve by definition of derivative if f(x)=x+Vx AND also Find x? w.r.t x*

A: fx=x+x Now by the definition of derivative, we have…

Q: Find the equation of the line tangent to the graph of y=4ln(x) at x=3.

A: Equation of tangent line

Q: What is the equation of the line that crosses the y-axis at 2 and h. a unit rate of ?

A: We have to find the equation of the required line. The required line crosses the y axis at 2, that…

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

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Q: I'm trying to find the derivative of  y = x * e^x

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Q: find the derivative of the function  F(x)= e^x/e^x + 8

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Q: Find the derivative ofe 11. D[(4x – 5)']

A: Given query is to find the derivative of thw expression.

Q: What is the slope of the line tangent to the graph of h(x)=sqrt(x) at x=3?

A: I have given the formula for finding a slope of tangent line below the proof  And it is used in this…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.