Problem 4. Find the total derivative of the following function: df dr. af of dy + dr Dy dr F(x,y) = (x²-3y)-(x+y³) if y=2x² + 3x

Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

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Q: 5. Use the definition of derivative to find derivative of ƒ(x) = (D + 2)x –- (C + 2)x². D=7 F=7 C=2

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Q: 1. Determine the slope of the following functions. į. f(x) = 4x³ + 5x4 - 9x + 2 f(x) = sin(3x) - 5x³…

A: We determine the slope of the following functions.                          i. f(x) = 4x3 + 5x4 - 9x…

Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: Give two different interpretations of the derivative of the function y = f(x) at x = a.

A: If f(x) represents a quantity at any x then the derivative f′(a) represents the instantaneous rate…

Q: If a = 1 − v^2 and both x and v are zero when t = 0, show that x = −1/2ln(1-v^2) and hence find v^2…

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Q: d g(r)= 3re³ %3D e y= e² – e-z 5 f. 8- 3+ el

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Q: The derivative of a function at each point is itself. y=kex

A: To find out the derivative of the function.

Q: Find the derivative of the following equations 1. y = Va? + x²

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: f (x) = x³ + 4xª + 3x³ – x² + & 1. ,2 -

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Find the equation of the line tangent to the graph of the function at the indicated point f(x) = x?…

A: Given curve :

Q: 12. Find the derivative of the following function. y = 71n(x -4) a. x3-4 b. Зx? х* c. d. 21x?

A: To find the derivative of the below function.          y = 7ln[x3 – 4]