Find the derivative of the following trigonometric functions and simplify if possible. Box your final answer. y = 3 sin x - 4 cos x

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A: Evaluate the integral  4sec2x/(tan2x+2tanx+5) 

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A: Splitting the numerator

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A: To evaluate the given integral.

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A: First we find singular points.  Follow step 2,3 . 

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A: Given: f(x) is increasing and fx>0 on the internal K. If f'x>0 then the function f(x) is incre...

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A: Note that the given function f(x) is said to be continuous at "x=a" if: limx→af(x)=f(a)

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Q: 10 Which of the following is the derivative of g (x) = x2 -10 g (a) = x3 O g (2) = -10 d (x) -10 O g...

A: Question is solved.

Q: the function. Show complete

A: We will solve the integral. 

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A: The solution is given in the next step.

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A: answer of given question is in step 2

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A: f(x)=x4-7x3/2 Differentiating with respect to x f'(x)=ddx(x4-7x3/2)=ddx(x4)-7ddx(x3/2)=4x4-1-7*32x3/...

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Q: x²dx Evaluate x2Vx2-4

A: Using standard formula for integrating the given indefinite integral

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Q: Find a mathematical model for the verbal statement. (Use k for the constant of proportionality.) Fo...

A: This question can be solved using the concept of changing proportional relations into equality.

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A: Given integral ∫xx+103 dx 

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A: 44. Solution :2x+y=-4   .... 1-2y+4z=0 .... 23x-2z=-11   .... 3equation 2 1+24x+2y-2y+4z=-84x+4z=-8x...

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Q: 6.) Find the directional derivative of g(x,y)=Vx² +y² at the point P(3,4) in the direction of v (3,-...

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Q: A boat starts off 179 miles directly east from the city of Morristown. It travels due north at a spe...

A: solution:-Boat started from O city of Morristown reaches the point A 179 miles due East and then it ...

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A: This question is based on vectors.

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A: I have stated the used formulas in the solution

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A: Topic:- differential equations

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Q: Find all absolute maxima and minima for the function y = x + sin(x) on the interval [0, 27].

A: Given function y=x+sinx    ;  0 , 2π