4. Find a particular solution of x' = [ +1 ]] = + [8 sin ³]. sint]. Hint: xp = x(t) [X-¹(t)f(t) dt is a particular solution of a' = Ax + f.

Q: ne hundredth derivative of p (x) (x + x³ + x')1º (1 + x² )11 (x³ + + x Justify ya

A: P(x) = (x+x5+x7 )10(1+x2 )11(x3+x5+x7) Here, (x+x5+x7)10  will have x70 as leading degree. (1+x2)11…

Q: 2. Find the derivative of the following functions and write the down the inner and outer functions…

A: Solution: 2.(a) fx=2x5-4ex

Q: 28. Show that tan z = sin(2x) + i sinh(2y) cos(2x) + cosh (2y)

A: We can show the given identity.

Q: f(x) = 7 exp[ cos (5x)] '(x) = ]

A:

Q: s¯¹(x + 1) − √√14 − 3x², find ƒ¹(x). If f(x) = 3x cos

A:

Q: x3 C. g(x) : et

A:

Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: Find f if f'(x) = 2 + cos(x), ƒ(0) = 10, ƒ(π/2) = 6. 2 f(x) = x² − cos(x) – (n - + - (x + 10 ) x +…

A:

Q: Find the derivative of the function. y = [x + (x + sin²(x))6]4 2 63 y' = 4 x + x + sin x • 1+4 x +…

A: Please see the attached image for the solution.Note that a series of Chain Rule for Differentiation…