: Mark all the ODEs in the list for which the function y(t) = cos(t) is a solution. A) y' = sin(t) B) (y)² + y² = 1 C) y' = y² - t D) y" =-y

Q: 12 3. (sin x)y' +y cos r = r sin a,

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Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Find y' at the point (6, 6) where x sin(x? – y²) + 33 = x? – 3.

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Q: ei=e*(cos(y) + isin(y))

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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.…

Q: Find y" for the following function. y = 4 cos x sin x y" = У'-‑

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Q: f(æ) sin(x) T Given f 5 and f' 6. Also let g(x) f(x)cos(x) and h(x) Answe the following: T a) g' ()…

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Q: Differential Calculus Find the third derivative of the ff: 1) y x 1-ex 2) y = 2ex - 8x 3) y = 6ex -…

A: We have to find the third derivative of the given function.

Q: If y = -cos(2t), then y(5)= ?

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Q: y" y'' +(cos xc)y' + ну =0

A: As per the question we are given the following second order homogeneous differential equation : y''…

Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern…

A: We have to find the differentiations of the give function and find y101.

Q: IV. Implicit differentiation 1. xy + y? = 1, find y? 2. x²y – xy? + x² + y² = 0, find y' 3. x? – xy…

A: Given: 1.xy+y2=1 , 2. x2y-xy2+x2+y2=0 3. x2-xy+y2=3 4. x3y+xy2=3 and x=1

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Compute Each Derivative: 1) d tan¯¹ (1 + e²x) dx 2) x²cos-¹(3x4) d dx 3) x(sin-¹(x))² dx

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Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: Let y = sin (x + y), find y'.

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Q: ) Find y as a function of x if x?y" + 2xy' – 42y = 0, y(1) = 5, y'(1) =-3. y =

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Q: Find y' and y". y = cos(sin(90)) y' %3D %3D

A: We have to find

Q: let y=[cos(2x-π)]3 Find y' at x=(π/6)

A: Compute the derivative as follows.

Q: use the Chain rule to find derivative: a) y = cot(412 +9) b) y = y = cos (e?) c) d) y = cos(x²) +1…

A: Solve the givens

Q: 3. (a) Determine whether the function y=1-cosx is even, odd or neither. (b)Find antiderivative of 3…

A: Consider the given function as y=1-cosx. Check the function is odd or even as follows. let…

Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

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Q: 1) Determine the derivative o a) f(x) = -4e*² b) y = cos(3*) c) g(x) = -2 sin3 (2x) %3D %3D

A: Note: Multiple subparts are given, we are answered with first three parts only, if you need more…

Q: O Find the derivative of the following functions: L 2+3 (a). f(z) = 2-3 (b). f(z) = 2 tan (z) – 7…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: a) Find the derivative of the following functions: i) f(x) = x Inx ii) f(x) = iii) f(x) = 1 4* iv)…

A: Solution:-