tan (X) where : Let z=f(x,y) = (10 + 23x)y" where : 13 - e (t – 1) + tan'(t) , and y= (2- t) e'- 13(t – 1). -(t) , and y= (2-t) e' – 13(t – 1). X: 2 e dz at t= 1. dt Use the chain rule to find

Q: 1 (D²-3³e*f"(x) =e³* (x) (D² - 3) O O

A: If we take f(x) =x^3/6 then the equation doesnt hold

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

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A:

Q: The equation cos (10x) = sec (50y) defines y as an implicit function of x. If it is known that, y'…

A: Given: cos10x=sec50y To Find: if y'=10sin10xgythen gy is equivalent to: Concept: i. ddxcosx=-sinxii.…

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Q: Find f. a) f '''(x) = cos(x),    f(0) = 7,    f '(0) = 8,    f ''(0) = 8   b) A particle is moving…

A:

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A:

Q: y" (t) - y(t) = 4 cos(t) ;y(0) +0 , y'(0)=1.

A: The objective of the question is to solve the given second order differential equation with the…

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A:

Q: Vx+5 1. State the domain of f(x) = 10° using interval notation.

A: The given equation is

Q: Let h(t) = tan(3t + 8). Then h'(5) is and h"(5) is

A: As we know that the chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1   Given: ht=tan3t+8 Now…

Q: Find r'(t). 13 r(t) = 3 cos (t)i + 5 sin (t)j + k %3D r'(t) %3D

A: Given:

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: r' (t) × r´ (t) to ||r' (1) × r´ (1)|| Use the formula B (1) = T (1) × N (t) to find B (t) , and…

A: Given that rt=sint-tcosti+cost+tsintj+48k. To find Binormal vector B(t).

Q: Hence, using chain rules find y' i. y = sin(2x² + tan(6x² – x)),hint: u = 2x² + tan(6x² – x) ii.y =…

A:

Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

A:

Q: If f(w) ) = cos¯¹(7w¹), find ƒ'(w). Use exact values and don't forget the chain rule. f'(w) =…

A:

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: Find the GS for y""+y"+y' + y = 1−x + e* - COS X

A: Given differential equation y'''+y''+y'+y=1-x+ex-cosx

Q: Find f. f'(t) = sec(t)(sec(t) + tan(t)), f(t) = - 1/2 <²<= // ¹ ( ² ) = -3

A: Given that, f't=sectsect+tant, -π2&lt;t&lt;π2, fπ4=-3 We have to find the function ft

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

A:

Q: solve this equahon: Y' CH)= 2y Cf) CyCE) -) y (6):0

A:

Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

Q: Determine r (x) if r(x) = (arccot(x))".

A:

Q: 4. Let f(x)= 5Vx and g(x)= 4 + sin x. (a) Find (f ° (x) and (f ° g'(x). (b) Find (g ºf)(x) and…

A:

Q: Find f. f'(t) = sec(t)(sec(t) + tan(t)), = -1 2 (t) = tan(t) + sec(t) – 1- V2

A: