Use the fplot command to plot the function f(t) = Vlcos(3x)+ sin (4x) in the domain -25 x S2.

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

A:

Q: Use implicit differentiation to find dy and xp 4x² + 3y² = 9

A: the given equation is 4x2+3y2=9

Q: find thedifferential dy of the given function. y = sqrt (36-x ^2)

A: Given : The function y = 36 - x2.   To find the differential dy.

Q: Find the derivative of the function. (S h(x) = %3D 8x2 + 9

A:

Q: For the function f(x) 5x3 – 8x? + 8x, Step 2 of 2: Find the equation of the tangent line at x = 1

A:

Q: Use the Chain Rule to find the derivative. y = (t2 + 3t + 1) -5/2

A: Here given y = (t2 + 3t + 1) -5/2

Q: The second derivative , for the function 7y+ 13z 3a2 is O y = 9

A: Given query is to find the second derivative of the function.

Q: There is no point on the graph of f(x) = 3x2 4 at which the tangent line is y = 12x- 2. Select one:…

A: We have to consider gi condition is true or false

Q: Find the direction in which the function is increasing most rapidly at the point Po. f(x, y) = xey –…

A: To find the direction in which the function is increasing most rapidly.

Q: Find the derivative of the function. A y = 7tan-(x - V1 + x²) %3D (2* * I^ -

A:

Q: Find the direction in which the function is increasing most rapidly at the point Po. f(x.y) = xy? -…

A: Given,     f(x,y)=xy2-yx2

Q: What is the domain of the function f(x, y) = x² /ỹ – In(x)?

A: topic -  function domain and range

Q: Find Fxxygy for the function Fory)-J*J€nx-x]

A: We havr to find the derivative.

Q: Hiw Find dy for the followng functions- 1-5x +X 2+x 3. y= lacsinfe}} %3D

A:

Q: Given f(x) = vx +8, find f' (-4) using the definition of a derivative. Provide your answer below:…

A:

Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: The line tangent to the graph of ƒ

A: formula used: The equation of the tangent line at (x1, y1) is y-y1=m(x-x1) where m is the slope of…

Q: Find the derivative using the definition. a. f(t) 2t+1 b. g(x) = 2x² +1

A:

Q: Create a 3-D plot of the function sin(/x² + y²) Vx² + y² for -8 <x5 8 and –8 < x < 8.

A: Note: Here, we are considering -8 ≤ x ≤ 8 and -8 ≤ y ≤ 8 rather than -8 ≤ x ≤ 8 and -8 ≤ x ≤ 8. We…

Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

A:

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: Which of the following is the x-coordinate of a relative extremum of the function f(x) = = Arct…

A: We will use first derivative test to determine the extremum of the function.

Q: Evaluate the function: dx ¤(1+x?)

A:

Q: Find the derivatives of the functions in Exercise

A: Explanation: Given that,  w=(2x-7)-1(x+5)     Formula used: According to the product rule of…

Q: e. Find the point(s) on the graph of f(x)= 5x³(4x² – 60) that have horizontal tangent lines. |

A: Any function have horizontal tangent line at points where derivative is zero

Q: Consider the function x + 3 f(x) = + V9+ 3x 6 – x Use the definition of derivative to find f'(0).

A:

Q: Q1) A) Find the tangent equation for the function f(x) = Vx² + 5 at =2 ?

A: To find  The tangent equation for the given function

Q: Find the inflection point(s) of the function f(x) 16x + 36x + 17x + 5. Show = 2r1 the work.

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: Find the differentiation and provide a complete solution a. f(x)=x2√1-x2 b. y=tan3x

A: See this diff and provide a complete solution in below

Q: Use the First Derivative Test to find the x-value(s) at which the function f(a) = + 4x? 2 9x? + 4…

A:

Q: Plot the following functions 1. y = - V2x +1

A: x y=-2x+1 -12 0 0 -1 1 -3 2 -5

Q: The derivative of the function y = tan(In(vx2 –- 6x + 1)) is: |

A:

Q: Find dydx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

A:

Q: Find the analytic function whose imaginary part is v =2xy

A:

Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True…

A: The given function is f(x,y)=1+x2+y21-x2-y2

Q: g(t) = 8t3 – 4t² + 12t – 3 %3D

A: This question is based on diffrentiation of function.

Q: 二D f(x) Vx3 x3+6x²

A: Given fx=x3+6x2 Rewriting the equation: fx=x3+6x212

Q: Use the definition of the derivative to determine dx (ax² + bx + c), where a, b, and c are…

A: NOTE: Refresh your page if you can't see any equations. . the definition of derivative is  here we…

Q: f(x) = + 3, X with 0 < x< 3

A: The length(arc-length) of the function is given by: L=∫ab1+(f'(x))2dx

Q: Use the definition of the derivative to find: f(x)= 1/x^3 g(z)= z^4 - 8z^2

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

Q: Use the Product Rule to compute the derivative: i (* + 1)(t + 9))|t- t=-9

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 +5 at =2?

A: The given function is; f(x) = √(x2+5)

Q: Find an equation for f(x) using the secant function. f(x) =

A: NOTE: Refresh your page if you can't see any equations. . the secant function is in the form of as…

Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ?

A: The equation of the tangent using the slope intercept is y=mx+b Where 'm' is the slope of line and…

Q: f(x) = + 2x' with 1 < x< 2

A: Given: fx=x36+12x with 1≤x≤2

Q: Find the intervals where the function f(x)= x^2e^3x is concave up.

A:

Q: Find ☆ f'(x) using using derivative rules. f(x) =Dx+ 2 to 11

A:

Q: Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f. f(x)…

A:

Q: How far is the object away from the origin when it fırst changes direction on the interval 0 <t< 3?

A: Given: An object is moving along the x-axis. At t=0, v(t)=sin2t, for 0≤t≤3

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: