Given f(u) =u/u2 - 1 and u = g(x) = 4x2 + x + 4, find (f o g)'(0).

Q: If f(x.y) = In(x² + y²) + find fr and fy -

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Q: Find the differential d4y of the function y=x5.

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Q: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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Q: B) Findfor the Implicit function: dx x² - sin(xy) + y² = 5xy

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Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: If F(x)=sinx+6x2−4 is an antiderivative of f(x) then f(x)=

A: If F(x) is antiderivative of f(x) , then f(x) is derivative of F(x) .

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y? + z²; x = psin o cos…

A: We have to find derivative of given function by using chain rule.

Q: Given that the first derivative of x^81+y^81=-36 is given by dy/dx=kx^c/y^c,what is the value of k?

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Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: The total derivative of f(x,y) = e2x +5y is df =

A: Consider the following function: fx,y=e2x+5y Total derivative of function:…

Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

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Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Use the appropriate form of the chain rule to find the derivatives. 7x2 + 7y? + z²; x = psin ø cos…

A: This question is based on Partial derivatives.

Q: f(x) = 9x3 + 4x.   Find the differential of the function.   dy =?

A: Given , y=fx where fx=9x3+4xwe have to find the differential dy

Q: Find the differential d4y of the function y=x4.

A: Given function is

Q: Find the differential of the function y = f(x) . f(x) = (5x² + 7)/3 dy =

A:

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: B) Find for the Implicit function: dx x2 - sin(xy) + y² = 5xy

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Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

Q: For f(x, y) = 2y3 + x² – 4x – 4xy – 9, find the critical points and use the - Second derivative test…

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Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: If f(x)dx = 32, then f(t)dt : %3|

A: Here, Order of limit has been exchanged with each other.

Q: Find the differential d3y of the function y=x2ex.

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Q: If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

A: In this question we have to compute kf(1).

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: Find the linear approximation L(x) of the function g(x)=  ∛(2+x ) at a = 0 and use it to approximate…

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Q: Find the differential of y=x^4-2x^2

A: Given query is to find the differential of the expression.

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: Let y = f(x), where   f(x) = 4x2 + 6.   Find the differential of the function.   dy =?

A: Given: y=fx=4x2+6 now differentiating given function with respect to x

Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: Let y = f(x), where   f(x) = 5x3/2 + x1/2.   Find the differential of the function.

A: The given function is

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

A:

Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: Find the linear approximation of f(x) = Vx at xo = 27.

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Q: g(x) f(x) - sin(2²) dt, find f(x). = J

A: To Find: f'(x)

Q: Find the second derivative of the function. x4 + 6 y = x2 a²y 36 O A. = 2 - dx2 d²y 36 OB. = 2+ 4 X…

A: We have to find the second derivative of the function: y=x4+6x2 Rewriting the function,…

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;

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: