Differentiate y = cos³x³ ,33

Q: Write 2 cos(3t) + sin(3t) as Rcos(wt - ). |

A: Here we will write in the form of Rcos(ωt-∅),

Q: * Evaluate. [12 [20x cos(5x² - 1)]dx

A: The given integral is   ∫20xcos5x2-1 dx We solve the integral using proper substitution .

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A: We know that integration of xn is xn+1/n+1.       Here i attached solution of this question.

Q: • y = sin¬(10x) %3D

A:

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

Q: Find ∫cos7 x dx.

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Q: Determine D103 (cos 2x).

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

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Q: 2. y = Ce*cosx + C2e*sinx

A: It is given that y=c1excosx+c2exsinx. The derivative of y=c1excosx+c2exsinx is computed as follows,…

Q: Differentiate y=(1-cosx)/sin2x

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Q: Find y' and y". y=2sin4x-cos(8x-1)

A: Let's find.

Q: Find if y cos²(xx) %3D

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Q: Evaluate fe.cos 2x dx

A: ∫e3x cos2x dx

Q: 3t test cos 6t

A:

Q: Evaluate ∫  (sin8t +20 cos9t) dt.

A: Use the formula for the integration of sin t and cos t. ∫sin t dt=-cos t+c ∫cos t dt=sin t+c

Q: cos³tdt dt 1-sint

A:

Q: (b) Differentiate y cos-1 23

A: Differentiate the given y with respect to x.

Q: find y = (cos(x))os®)

A: Let y=(cos(x))cos(x) By using the logarithmic differentiation, Apply logarithm on both side…

Q: 6. cos x sinỗ xdx

A:

Q: Differentiate: y = 8 cos (16x*)

A: Here we  must know about the chain rule ddx(cos(x))= -sin(x) ddxxn= nxn-1

Q: cos 2xdx CoS Vsin2x

A:

Q: 2) y= e** (c, cosk + C2 sinx)

A:

Q: 4sinx •cotx / cos2x + 1

A: You know:

Q: cos e de O 4

A: Given

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A: The objective is to find the value of given integral.

Q: Find y' if y=Cos (sinx)

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Q: y= sin2x,

A: Given equation is: y=sin2x Differentiating with respect to x we get, dydx=ddxsin2x⇒dydx=2cos2x

Q: 10. If cos(x + y) = 2x- 2y, find y'.

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Q: Integrate x3 cos(x4)

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Q: cos 2x 6. 4

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Q: coS 3dv

A: on solving this we get

Q: Evaluate ∫cos5 x dx

A: Evaluate: ∫cos(5x)dx

Q: Evaluate: [ cosx dx.

A: Here we have to evaluate I=∫02πcos5xdx

Q: State the amplitude of y = -3 cos(4x) +6 1. 6 2. -3 3. 3

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Q: Evaluate  sin2x*cos2x dx

A: Given that: ∫sin2x.cos2x.dx

Q: write in terms of x: cos(sec ^-1x)

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Q: Evaluate fcot (x) cos²x dx

A: The given integral: ∫cotxcos2x dx.We need to evaluate the above integral.

Q: Differentiate  cosx/x

A: The given function is f(x) =(cosx)/x       = x-1.cosx

Q: 2(csc270°)+7(cos90°)^2+sec0°=

A: Solving by trigonometric ratios we have

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Q: Integrate  cos3xcos2x

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Q: Differentiate: y = 2 cos² (x² + 2) %3D

A: Given that, y=2cos2(x2+2)

Q: Evaluate cos (4x) dx.

A: