df-1| For the function y = f(x) = x + 3x + 1, > 1.5, find dy (f-)'(3) = %3D

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A: We use logarithmic differentiation

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Q: dy for y = x2 - 8. Q2) Find dx x-1

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Q: -(3x² + 10)e¯= d Evaluate dx (3x² + 10)e¯ª at x = 0. d (3x² + 10)e dx x=0 II

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Q: G3- y²sinx+3e3*)dx+(3xy² +2ycosx+)dy=0 |

A: In this question, we have a differential equation of the form Mdx+Ndy=0 Here we have to check the…

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Q: dy EX-2- Find for the following functions: dx (x² + x )(x² – x +1) e) y= x² - 1 x² +x- 2 f ) y = -

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Q: S For x 1/2 x-x3 dx and using the substitutionu=x1/2

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Q: Find the value of df-1/dx at x = f(a). f(x) = x 2 - 5x + 6; a = 5 1 1 10 1 15 O 5

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Q: dy find for the following functions: dx (x²+x)(x²-x+1) y = x3

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Q: dx :- x = ey/2 x3 dy 1- 2

A: First we need to reduce it into linear differential equation form by using substitution method

Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

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

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Q: Q4 Find dy for all of : dx 2- y = 3 x(x-2) x2 +1 1- y = xvInx

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Q: dy Find for x'y' +e2x = -3e" -1. dx

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Q: dy 3. x. e*y. + y. e*y - 4x3 = 0 dx -

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Q: dy Find of the following function: dx (x² + 1)° e-2+

A: The derivative is calculated as follows:

Q: 1 df For the function y = f(x) = x - 4x – 3, x > 2, find dy 1 (f ')'(– 1) =

A: f(f-1(x)) = x is one of important property  of functions Let y =f-1(x) f(y) =x Differentiate both…

Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

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Q: d²y Find for the following function. 2 dx y= (3x² +1) -5 d²y dx² =

A: Given: y=3x2+1-5 To find: the second derivative of y. The power rule of differentiation states that…

Q: (-4x-12) dx For J x+10)³ (x-4)³ F(x) – 1. What is F(3)? -

A: Given: ∫-4x-12x+103x-43dx=Fx-1   ...(1)

Q: ¡xr-¹e-λx, x>0, r,λ > 0. Given f(x) Γ(r) 1. Find f(x)dx.

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Q: Q2: Fill the blank: 1) lim (1+)5x x48 4x 2) lim x.e-3x = X-8 3) (csch-¹x³) = = 4) ₂° e-*dx 5) S-…

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Q: dy What is if the function y = f(x) is implicitly defined by the equation 5x + 3y² = 4y + 2x² - 5?…

A: For implicit differentiation , both sides of the equation are differentiated simultaneously.

Q: -4x+2 Integrate f6 dx with respect to x using the substitution method. (-2x2+2a-2) COMPLETE THIS IN…

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Q: = 2-x² and f'(2) dy when x = 1. dx 8. Let y f(1+ Ju), - 3.Find

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Q: N= 8%° + 3s $1

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

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Q: d²y B Show whether y = Ax² + · x2 is a solution for x2- dy + x dx + 3y = 0 or not. dx2

A: If y=Ax2+Bx2 is a solution for x2d2ydx2+xdydx+3y=0...(1) then it satisfies equation (1).

Q: |(2 f(x)+3) dx=19 f(x)dx then equals?

A: ∫afx+bdx = a∫fxdx+∫bdx

Q: d² y Q2/ A/ Find dx2 in terms of x and y (implicit derivative): Vx? + y? = 1

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Q: dy Q1) Find dx for the following function x²(x² + y²) = y²

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Q: d²y 1. dx² - dy - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: Find d-y for the given function. dx2 y = x - sin(x) 6 dx2 %3D

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Q: d (1.5ƒ(x))|a=2 dx 10- -х — 2. The line tangent to the graph of f at x = 5 is y = d (4f(x)) x=5-…

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Q: dy Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) x2+1

A: See the details solution in below

Q: 3 d²y If the functions are x = e-t and y = t+t + 1. Determine its dx2

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Q: Find the function y(x) satisfying =4 dy =4x-3 and y(6)30. dx The function y(x) satisfying --4x-3 and…

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Q: -kx xn-1 dx ,n> 0 k>0

A: The given problem is to evaluate the given improper integral.

Q: I am not sure how to do this. For the linear function y=f(x)=1x−3 Find df/dx, at x=5

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Q: e-k* xn-1 dx ,n > 0 k> 0

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Q: For -e y=ln 2t find y ' when x=e-

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Q: Compare dy and Ay for y = -4x² – 3 at x=-1 and dx = Ax = -0.06. Give the answers to four decimal…

A: Given:the equation of y is y=-4x2-3 at x=-1  and dx=△x=-0.06To find:Find the value of dy…

Q: dy Find for dx 1 y=-=-72-8√x x

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Q: Q4 (a) Evaluate by solving the work for (i) Só xe-*dx. -5 29-3x ·dx. x2-x-6 (ii)

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Q: Find the value of df-1/dx at x= f(a). f(x) = x² - 4x + 2; a = 5 1 O A. 6 1 O B. 14 1 OC. 10 O D. 6

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Q: -1 df For the function Y = f(x) = x² + 2x + 4, x > – 1, find dy y=7 (f-1)'(7) =

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Q: Let ƒ(x) = x2 - 4x - 5, x> 2. Find the value of dƒ -1/dx at thepoint x = 0 = ƒ(5).

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