*Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: Find the derivatives of the function x=a (cos t + sin t ) ,y=a(sin t -t cos t

A: To find the derivatives of the function

Q: Find dy/dx if 3 (cos y) (sin x) = y

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Q: Let y = cot (csc2x/x3+5). Find

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Q: find y' y=cos(3x)+cot(5x)

A: We have to find derivative of f(x),where f(x) is given by:

Q: Determine the equation of the line tangent to y = (sin x)²(cos x) at the point (5,0).

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Q: sin(y) = -5x dy Also, dt 10. dx Find when y = -T. dt

A: Consider the following: Differentiating the function with respect to x on both sides, we have,

Q: y' = 2 - sin t

A: Given that y'=2-sint. solve the above differential equation as follows.

Q: Find T, N and B for the curve 7(t) (2 cos(2t), 2 sin(2t), 5t) at the point t = 0 Give your answers…

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Q: Evaluate dy/dx if y = (sec2x - tan2x)/(2cos2x-1)

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Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: Find dy/dx y = sec u, u = X- COS X -

A: Given : y = -secuu = x-cosx

Q: Find points of horizontal and vertical tangent lines r = 1- cos(0) %3|

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Q: cos(xy) + sin(x/y) = 2y find dy/dx at point (pi,1)

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Q: sinhçc+y)= sinhx.coshyFcoshx:sinhy

A: Here we have to prove that   sinh(x+y) = sinhx.coshy + coshx.sinhy    and   sinh(x-y) = sinhx.coshy…

Q: Find the following using the table below. x 3 4 f(x) 3 5 1 f'(x) -5 2 -4 1 g(x) 1 4 2 3 g'(x) 3 2 -1…

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Q: 2. y = tan-1(sin 3x) + cos-(cos x)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…