SUBJECT: DIFFERENTIAL CALCULUS FIND THE FIRST DERIVATIVE OF THE FOLLOWING FUNCTIONS. SIMPLIFY YOUR ANSWERS. y = cos4x – sin4 x y = x3   –  x2cos x  +  2x sin x  + 2 cos x NOTE: Make the solution detailed and clear in a sheet of paper.

Q: Calculate the derivative of y with respect to x when sin(x + y) = 5x + 4 cos(y). (Use symbolic…

A: topic- derivatives

Q: Problem #10] A kite 100 ft above the ground is being blown away from the person holding its string…

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Q: 5x-2 Find the member of the curve whose slope at any point is y+s point (3, 2) and passes through…

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Q: The solution of the differential equation=1-x+y-xy is: dx

A: To solve the given differential equation

Q: The points R(-1, 1, -3), S(3, -3, 6), T(0, 0, 10), and U(2, 4, 7) are the vertices of parallelogram…

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Q: 3. Find the equation of the tangent to y = 1-x² 3x+7 at the point where x = 1.

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Q: x² dx -1 (2x²+2x+1)² sº₁

A: We have to evaluate the integral. ∫dxa2+x2=1atan-1(xa)+c

Q: дz дz Suppose z is a function of r and y and tan(√x + y) = e²². Determine and 3x ду

A: given function tanx+y=ez2

Q: Solve the applied minimum and maximum problems. Make sure to sketch figures to illustrate the…

A: Use minimizing concept

Q: . Find the derivative of a composite function using the Chain Rule or General Power Rule. 1.)…

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: The doubling time of an investment with continuous compound interest is 12.5 years. If the…

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Q: 6. Find the intersection of the line I and the plane . 1:7=(4,-1,4) +t(5,-2,3) 2x+5y+z+2=0

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Q: 4x+8 (x+2) ³ 3). D. Ba -dx

A: This is a problem related to integration. Based on the general formula and concept we will evaluate…

Q: Physical Applications of First-Order Differential Equations A body at a temperature of 50° F is…

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Q: lim.. lim X→+∞0⁰ In5 x x² In 1000 X 5 X X→→→→+∞0

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Q: Two capacitors with capacitance of 6 μF and 4 μF are connected in series across a 100 V dc source.…

A: Question- Two capacitors with capacitance of 6 μF and   4 μF are connected in series across a 100 V…

Q: A drag racer accelerates at a(t) = 96 ft/s2. Assume that v(0) = 0 and s(0) = 0. a. Determine the…

A: To find out the distance/position function.

Q: 2 Brad wants to buy a coffee machine for his café. The advertised price is $3200 including GST. When…

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Q: Find the absolute maximum and minimum of the function f(x,y) = 2x² - 4x + y² - 4y +6 on the closed…

A: Solution: f(x,y)=2x2-4x+y2-4y+6 the vertices of the triangle by joining the given lines are (0,0)…

Q: e) Evaluate the following limit at infinity and show your work. 3x3-4x a) lim x→∞ x²-2x³

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Q: how did you get the final answer??

A: Let's find value of rate of change of slope with respect to x.

Q: Convert each pair of rectangular coordinates to polar coordinates where r>0 and 0 ≤ 0 <2. 1) (-3,0)…

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Q: () 2 1- (x+6) (x+2) 2

A: The given integral is:…

Q: Find the area under a curve whose equation is y = x³-3x²-x+3 From x = 0 to x = 2

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Q: The are of the parabola y=x² from (1, 1) to (2, 4) is rotated about the y-axis. Find the area of the…

A: Let's find area of the resulting surface.

Q: 5) Find the volume of the parallelepiped defined by vectors u = [1, -3, 6], v[-2, 5, 6] & w = [1, 2,…

A: Calculating the volume of parallelepiped

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e5xy = sin…

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

Q: Use the series to evaluate the limit tan-¹ y - siny lim y→0 y³ cosy

A: Expand series and solve

Q: Drogon (The dragon) wants to fly to an island which is 1200 km away at a heading of [N42°W]. There…

A: We have to draw the diagram and time required.

Q: 3. Find the member of the curve whose slope at any point is and passes through the point (1, 1)

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Q: Jack has 13 cards printed with the letters from the word “UNDERSTANDING,” so that “U” is in one…

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Q: 3 fin [ ха Txx² 2 - 1/2 to

A: To evaluate: ∫13lnx21+x212dx=∫1312lnx21+x2dx=12∫13ln x2-ln (1+x2)dx=12∫13(2ln x) dx-12∫13ln(1+x2)…

Q: 2. Show that the function g defined by VVT y² + √² 2, is not continuous at (0,0). (z,y) = (0,0)…

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Q: 4. Determine whether the following statements are True or False? y = f(x)

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Q: 5. Find the general equation of the circle of curvature of the parametric equation X= ;y=+√6(t+1);…

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Q: Which of the following statements about the graph of f(x) = (2.25) shown above are true? Select all…

A: Given graph of f(x)=(2.25)x

Q: 1. Evaluate the given integral Q. Q 2= 1 L (₂² (x² - y) dy dx Your answer 2. Sketch the region of…

A: In the given problem first we sketch the region of integration for Q and then reverse the order of…

Q: 12. Find the integral of S (x². √(x² + ² =) dx

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Q: 11.) Solve using matrices and Gaussian elimination: x+y+z= 9 -x-3y + 2z = 10 2x + z = 9

A: Please see the below picture for detailed solution.

Q: dw ow For the functions w = xy + yz + xz, x= u + 3v, y = u- 3v, and z = uv, express and using the…

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Q: 2 x (1 + y²) dx -y (1 + 2x²) dy = 0

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Q: 3 Find x=x-12 lim. x-7-3 x2+ 8x+15)

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Q: In 1000 5 X limx→ +00 X

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Q: 32/5 y=x² 32 Find the area of the region bounded by the graphs of y = x² and y = 4x. 64/3 32/3 64

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

Q: √ and g(x)= )=x² Let R be the region in the first quadrant bounded by the x-axis and the curves f(x)…

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Q: Find all critical points of the function f(x) = 2x² 7x²2-2x+4* (Use symbolic notation and fractions…

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Q: 3 =+1)

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Q: 9 Use the shell method to find the volumes of the solids generated by revolving the shaded region…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: For each given functions, find the slope of the tangent at a given point using first principle…

A: We have to find the equation of tangent.

Q: Evaluate the following integrals: (show solution) a x² +2 b.) 1 x+1 x+√x c) f(sec x d.) e 4x 4x+1 x…

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