of of and da For the function f(t,a) = sin (8rt + 7a), find %3D - at

Q: c. f(1) d. Is f differentiable at x = 3?

A: Given The graph of function f as  To find: c. f1d. is f differentiable at x=3?

Q: rapidly at Po, Then find the derivatives of the functions in these directions f(x, y) = x²y + e" sin…

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Q: dy for the implicit function x' +xy - y² = -1 dx at the point (1, 2). Find

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Q: COS X continuous? 3x At what points is the function y=

A: The given function y=cos x3x

Q: 1. For the square root function f(x) = V¤, (a) calculate an equation for the secant line connecting…

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Q: Use the value of the given hyperbolic function to find the values of the other hyperbolic functions…

A: We use the following identities to find values of other hyperbolic functions:

Q: x3 for y = Differentiate. Find dx x-1

A:

Q: dy for the following functions : dx 1. Find 3(x – 1) (ans.: 5) Sec² /2x +7 15) y=\tan /2x +7 (ans.:…

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Q: r2x²+2x+1 Find the equation of the tangent line to the graph of F(x) = evy dy at x = 0. J sech x

A: We have to find the equation of the tangent line to the graph of F(x)=∫sechx2x2+2x+1eydy at x = 0.

Q: Using variable separable find the GS of dy 4x + ху? %3D dx y – x²y

A: Given that      dy/dx = (4x+xy2)/(y-x2y)  We have to find the general solution by using the variable…

Q: Find dy / dx by implicit differentiation. Then find the slope of the graph at the given point.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: The concentration of a certain drug in the bloodstream x hr after being administered is…

A: Concentration of a certain drug in the bloodstream x hr after being administered is given by-…

Q: dy using implicit differentiation dx 1. Find а. Зху + 4x2 + 5y? %3D 5 b. y + 2x³y* + 2y² = 3x = 3y2…

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Q: he maximum rate of change of f at the given point and the direction in which it occurs. f(x, v) =…

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Q: Q2-Use implicit differentiation to find y: a- tan xy = y b- tan?(y + 1) = 3sinx %3D

A: (a) Consider the given implicit function and use the chain rule to find the derivative.

Q: dy for the function y= Find dx (x-1)(x-2)* (x-3)' at @x = 4.

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Q: Consider f(x)=tanx a. Find the linear approximation of f(x) at a=pi/4 b. Use this to estimate…

A: This question can be solved using the formula of linear approximation.

Q: Given that f(x, y) = xy sin(x + y).Find all second derivative fxx,fxy, fyy, fyx.Show all your steps.

A: Given: fx,y=xysinx+y

Q: f'(rr), where f(t) = sint cost

A: Given function is ft=sint cost To find: f'π Solution: Product rule of differentiation is:…

Q: Evaluate dy and Ay for the function below at the indicated values. y= f(x)= 44 1-- x- 2, dx Ax = -…

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Q: A. Find the derivative of the function at o P in the direction of A f(x, у) — х — V3sec-1(2xy)at…

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Q: sin(r² + y* ) Find L for the functions: Əx' ay . (x.y) » (0,0) f(x.y) = (x.y) = (0,0)

A: Given- fx,y=sinx3+y2x2+y2      ,x,y≠0,00                      ,x,y=0,0 To Find- ∂f∂x and ∂f∂y for…

Q: (c) Use implicit differentiation to find y'(x) for (5+ y?) = x°y+ 4. Show all steps in your process.…

A:

Q: Q1 If z is a differentiable function of x and y which satisfy equation x3 + y3 + 3 x? siny tan z = 5…

A: The detailed solution is as follows below:

Q: Q4: Find the derivative of the function at Po in the direction of A 1) f(x, y) = 2.xy -3y, P.(5,5).…

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Q: dy Find dæ for implicit function x³ sin y – 3y4 = e4 + 6

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

Q: Find- for the following function dx x=a(cost + t sint).y=a (sint-tcost)

A: y=a(sint-tcost), x=a(cost+tsint) To find dy/dx.

Q: H. For the function f(x)= cos(ax), find all MVT Values 0<c <2 where f(2)-f(0)= f'(c)(a - o)

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Q: LH.S.-R.H.S. HW/ Brove-that: (1) 1-tanhf x sech'x 12 11

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Q: dt F(x) = | 6+ 8t Find the interval on which the curve is concave downward.

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Q: [ to y²-Xy flo dy 2

A: 1st we will use substitution and then integration by parts   ∫u.v dx=u∫v dx -∫dudx∫v dxdx

Q: Q:: Find for the following functions: - dx 1- y = tan/2\2x+ 7 (x²+x)(x²-x+1) 2- y =

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Q: Using the Power Rule Find the following derivatives.

A: Consider the following expressions: ddx9x5=ddx9x-5=9×-5×x-5-1=-45x-6=-45x6…

Q: f(x+h)-f(x) = lim 1. Use the delta method, dx for the following: dx to find h0 2 BONUS MARKS y = 5x2

A: We will use the definition of derivative as defined in question.

Q: lf f(x) = 3x sin x cos x, find f'(x)= To two decimal places, Find f'(2) =

A: f(x) = 3xsinxcosx find f'(x) = ? and find f'(2) = ? here first we use formula 2sinxcosx = sin2x and…

Q: dy for the function dx b. [. |The derivative y = cot-1 V14 – x²

A: Explanation of the answer is as follows

Q: Define a function L(r)=f (0)+xf' (0) for a functionf that is differentiable at x = 0. line at would…

A: Given function L(x)=f(0)+xf'(0) and differentiable at x=0

Q: Find all values of the constants m and b for which the function S sin x, y : тx + b, х 2п is a.…

A:

Q: Use the value of the given hyperbolic function to find the values of the other hyperbolic functions.…

A: cosh2x-sinh2x=1cosh2x=1+sinh2xcosh2x=1+2516cosh2x=4116cosh(x)=±414

Q: Q1) Find the derivative a) f(x) = arctan (e-2x) b) f(x) = [arcsin (2²)]³ C) f(x) = tan (lnx) + 52²

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Q: Q1. To solve this problem, you should use the function on the same line as your w value. w = 2 =…

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Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x – E) V3sec-1(2xy)at…

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Q: Q1- i) Show that cosh?x – sinh?x = 1 ii) Find the equation for the tangent line to the curve y = Vx…

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Q: 1. For the square root function f(x) = V, (a) calculate an equation for the secant line connecting…

A:

Q: Find the point on the curve f (x) = Vx that is closest to the point (2,0). Put your answer in the…

A: Use distance formula and differentiate and put zero

Q: 3 dK Use the definition of the derivative to find for the function K(z) %3D dz 6z + 1"

A:

Q: 5. For the function g(x) = sin(x), find all points – 1<c <1 where the MVT shows g(1) – g(-1) =…

A: To find the value of c using the mean value theorem

Q: ôf Find Ôx X for the function f(x, y) = ln sin| %3D +y² y

A: A detailed solution is given below.