(x – 7)2 3x2 (x + 2) Suppose f' (x) Determine where the tangent line to y=f(x) is %3D horizontal.

Q: The equation of tangent line of the function 21 x3 f(x) = e7e dt %3D 21 x at x=1 is V21 e3087 (x-1)…

A: Given function is  f(x)=∫21x21x3e7t2dt Since at x=1, upper limit of the integral is equal to lower…

Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

Q: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

A: Explanation and solutions is given below....

Q: Find an equation of the line tangent to f(x) =3 at x 3. %3D OA. y=xln 3+ (1– 3ln 3) OB. y=27(xln 3 +…

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Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: (2-4t) sin(팔) V17- cos(27t) 1. Given f(x) = dt, find the equation of the line tangent to the graph…

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Q: f(x)=x2+2  at (1,2)   Find the equation of the tangent line using delta method

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Q: 4. [ ]Find the derivative of y with respect to the given independent variable: Ins 7x (a) ex³y = 2x…

A: Given equation ex2y=2x+2y   As per our guideline, we  supposed to answer only the first three…

Q: Q1) Answer the questions by true or false 1) If y = In then the derivative of y is = (x2 + 3) * 2x…

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Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

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Q: In what directions is the derivative of ƒ(x, y) = (x2 - y2 )/ (x2 + y2 ) at P(1, 1) equal to zero?

A: Given, , the unit vector is , here directional derivative is given as,

Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: 4)* Find the derivative of f(x)= Arcsecr. %3D f'(x) = 4 rv.r* O None of the above O Option 4 f"(x)=:…

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Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: The given function is f(x, y)=y2-ysinx-x4.

Q: (a) Find the derivative of fix. y. 2) = x-xy-z at P1, 1,0) in the direction of v = 2i- 3j + 6k. (b)…

A: The directional derivative of a function f(x,y,z) at the point (x,y,z) in the direction of vector v…

Q: Find the partial derivative dz for the function z = cos(x³ +y²).

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Q: What is the derivative of (6 x+1)5 (4 x-21)16 (21 x-23)3 (3 x+25)4 y = In with respect to x?…

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Q: What is the equation of the curve whose tangent line passes through the point sec (In x) dx? (1,2)…

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Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

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Q: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: y2+y=x  Differentiating both sides with respect to x  ddxy2+y=ddxx    2y+1y'=1    y'=12y+1

Q: Determine the derivative of y=tan(cos-(4x)). -1 A y'=. 4XV1- 16x2 None of the given choices -1 y's…

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Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: Q. No. 5. Find the Derivative of the Given fur a) y= ev1n x( Inx) +2x b) f(x) = %3D a+x

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Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

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Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: 3/20 What is the equation of the tangent line to the function y = e*- arcsin) at x= 0 ? A) y- -(1+)=…

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Q: I. Determine the equation of the tangent line to the graph of f(x) V3+ 5t5 dt at I= 1.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Q /Choose the appropriate derivative for this function y = (x+ 1)2* dy = 2* (x + 1)2" - In(x + 1) dx…

A: Explanation of the answer is as follows

Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

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Q: -7/2 = 8. Calculate the derivative of y with respect to , if x/2 + y dy dx

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Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

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Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: Let fx) - V4X-3 vux-3 %3D O Find the arer age rate o ofe change in respect to x aver the intoy vel…

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Q: 3.9.27 Find the derivative of y with respect to x. y = sec 1(5x2 + 1). -1(5x2 +1), x > 0 dy %3D dx…

A: Please see the answer in Step 2

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

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Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

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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: