(a) PSD of U (t) = X (t) + Y (t) (b) Sxy (@) and Sxy(@)

Q: Find the derivative (df/dx) 1- f(x) = cscx - 4√x + 7y−² 2-f(x)=x² cotx-x-2 3-f(x) = (secx + tanx)…

A: We have to find derivative of given function.

Q: dy Find when y = a dx (a) (b) (c) (d) 2bx x4 + b² Arctan Arctan(2) 2bx ln a _ Arctan x4 + b² x In a…

A: Given y=aArctanbx2

Q: v=(*++1)(r+2) 11. (u)=(1+ \u)(u-u°)

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: (5) (sec-i x) =, d

A:

Q: Calculate the derivative of the function. f(x) = [(2x – 1)2 + (1 – x)°]? %3D f'(x) = %D

A: We will find the derivative using chain rule.

Q: nd and simplify 2² x² (f(x) g(x)). O d² O −(ƒ (x) g(x)) = ƒ” (x) g(x)+ f (x) g″ (x) Hint 2² -(f(x)…

A: Given query is to find the double derivative.

Q: dx" 2F₁ (a, b; c: x) = (a), (b) 2F₁ (a+n, b+n; c+n; x) 7

A:

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

A:

Q: ((x/y)/z)+(x/(y/z))

A: In mathematics, precalculus is a set of course that includes algebra and trigonometry to prepare…

Q: R(x)= 1 dt . 76 +4 Use FTC part II to find the derivative of the function

A:

Q: +8x-x +2x +1 (x² + 3)(x' +1)

A: SImplification of the given function helps to find the required integrated function. The partial…

Q: L=2-36X, y'co) =5, and ylo)=S x)

A:

Q: H (x) = VI-Soe? 2. %3D (f09) (><)= H (sc) %3D %3D 9(36) =

A: Given fgx=1-5x2

Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: Find the derivative of f (y) = 8 tan (y) V √y 8 8 √Y y4

A: The given function is: fy=8tany-y8-8y4y As we know that; The Sum/Difference rule: f±g'=f'±g' The…

Q: 7 (2+ x³)' Vx² – 1 (x2 + x + 1)* 3 d B : dx - 4

A:

Q: y=u (1+u³)* and u = (3x - 2)²

A:

Q: + If x? = x-y then, y *+y

A: Given  x2=x+yx-y first we multiply each side by x-y x2x-y=x+yx-yx-y     by dividing  x-y from x - y…

Q: First derivative of ₂ F₁(x): d a {2 F₁ (a, b; c; x)} = dx a.b с 2F₁ (a +1, b+1; c + 1; x)

A:

Q: DERIVATIVE

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

Q: Find f ′(a) f(t) = t^5 - 3t

A:

Q: f(x) b-a dx = 2 Prove f(x)+f(a+b-x) a

A:

Q: lo UcE - Uxx=0 4(x,0) = f(x) 4= (x2,0) = g(x)

A:

Q: 2dy+ydx=y3(x-1)dx (Bernoulli)

A: We have to find the general solution of differential equations

Q: f(x) = 4sin (1-3x2) + xcosx-9, then f'(x) = -24xcos (1-3x2)+cosx-xsinx True O False

A:

Q: y(t)=(2t-1)(5t-5)^-1, find y'(t)

A: Using Quotient Rule of Derivatives

Q: ,2, (x²–1)* Dx (1+8x)5

A: To Determine: find the derivative using chain rule  Given: we have y=x2-141+8x5 Explanation: we have…