d²y If y=cos 4xr, then at x = 0 dx?

Q: dy If y = sin='(cos x) then dx ||

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Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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Q: dy Find dx from the equation y = sin[cos xy].

A: Explanation of the answer is as follows

Q: dy dx ytsinx I+ CoS X

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Q: dy 7. dx cos(x + y), when x = 0,y = 4

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Q: dy If dx = COS s 2x, then what is y?

A: The derivative is given by dydx = cos2x                         ........(1)

Q: d²y Find 2 dx? y = sin 2x+cos² x

A: Using derivatives.

Q: Q2/Find dx of y = sin(e') + xtan-1x. %3D

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Q: dy соmpute dx for implicitly given function cos(xy) + 2y = x³

A: cos(xy)+2y=x3Differentiate with respect to x,-(sin(xy))y+xddx(y)+2ddxy=3x2

Q: dy 5. Find : (b) y = cos (11x³ + 5x). dx

A: The detailed solution is given below Thank you

Q: y=(4x -5x +6)(e-sin 2x), then find dy at x 0.

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Q: dy dʻy dx? cos x = 3 when x = - dx Find the original function y given that and y = 4 when x = 0.

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Q: -. Solve for dy/dx a. y = *+ sinx cos x † Sin X

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Q: b. sin 2xdy – 2(y - cosx)dx = 0; when x = 1/4, y = 0

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Q: dy d'y dx ' dx? 2. If y = sin 2x – 2 cos 3x,the find, at x 0

A: The given function isy=sin2x-2cos3xto finddydx, d2ydx2    at x=0

Q: dy at the given point. dx Calculate sin² (–5y) = x + y, - %3D 4

A: Given equation sin2(-5y)=x+y and point 2-π4,π4 The objective is to calculatedydx at the point.

Q: Q4: Find dy\dx if|cos?y +5y2 = x2

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Q: Find dy/dx given that y = sin(cos(x))

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Q: dy Q3) If y = In[sec 0 + tan 0) find- dx

A: To find dy/d(theta)

Q: The dy/dx for y=-4x+7 cos x d/dx (-4x+7 cos x )=

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Q: dy Find for: dx y = 5x[cos"(5x] -ī - 25x2

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Q: cinxo ) 2X. dy dx Find for y= cos ( Inx + e

A: We have to find the derivative.

Q: dy Solve Y for y=/4×(sin x) cos dx

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Q: y = cos s (2² + 7) dy Find dx dy dx

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Q: find dy/dx y = cos (x2)

A: Given y=cosx2 Applying derivative with respect to x: Using chain rule:…

Q: dy Let y=e* sin 3x. Show that 3e-2* cos 3x - 2y. dx -2x d'y = -13y-4- dr Hence show that dx

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Q: dy 4) Find dx when y² – x² + cos(x + y) = 0

A: As we know that the derivative of : ddx(xn)=nxn-1 ddx(cos(x))=-sin(x) ddx(f(g(x)))=f'(g(x))g'(x)

Q: dy 4 sin 2x, y = 2, when x = 1/2 dx

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Q: w= Cos (x+y) + Sin (X-4) Show that dy?

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Q: Find dy/dx in terms of t if x = te', y = -5t – 5e dy/dx = [

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Q: dy Find dx for y = 14x +5 coS x. d(14x+5 cos x)%3D

A: Formulas:1. ddxxn = nxn-12. ddxcosx = -sinx

Q: Find dy : (a) y = cos(1 Ix + 5x) dx

A: Topic:- calculus

Q: Find xer2 dy if dx = y sin x 1-

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Q: Q4: Find dy\dx if|cos'y +5y? = x?

A: The given equation iscos2y+5y2=x2to find dydx

Q: dy 7. Find ,y = cos³xsinx? dx

A: Given: y=cos3xsinx2 Formula used: Product rule of derivative: ddxf×g=dfdx×g+dgdx×f Power rule of…

Q: find dy/dx y Cos()= 2x+Y 2

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Q: dx/dy + sin'3 y/ cos'2 2x = 0

A: We are given : dxdy+sin3ycos22x=0⇒dxdy=-sin3ycos22x⇒cos22x dx=-sin3y dy Integrating both sides, we…

Q: b. sin 2xdy – 2(y – cosx)dx = 0; when x = n/4, y= 0

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Q: Find dy/dx in terms of t if x = t- 2, y = 2 + 1t dy/dx= [

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Q: dy (a) cos“ x cos y = CO dx

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Q: 2. If xy+Y find the value of dy dx2 5- at the point Co,-1)

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Q: dy about cosx+ylny= 0. dx Ask for

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Q: dy 4. = 4 sin 2x ; y = 2, when x = Tt/2 dx

A: Given a differential equation, dydx=4sin2x ; y=2 where x=π2 To find the general solution of the DE.

Q: Use this equation to find dy/dx. 8y cos(x) = x2 + y2 dy dx II

A: Given  8y cos(x)=x2+y2We find dydx

Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

Q: If Xy +y'=1, find at the point Co,-1) 4P dx 2 5- the value of

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Q: dy 7. dx = cos(x + y), when x = 0,y == 4

A: Differential equations, with substitution method and separation of variables

Q: Find (dy)/(dx) : y = e13x cos x

A: Given:y=e13x cosxFormula:ddxuv =uv'+vu'

Q: dy Find for y = - 12x + 5 cos x. dx dy %3D dx

A: We have to find derivative for given function.

Q: dy dx 2. 2X for y = cos (Inx + e) %3D

A: ddx(Cos(x)) = -sin(x)ddxex =exddx(log(x)) =1xddxxn=nxn-1Chain ruleddxf(f(x)) =f'(f'(x)) Here , In…