",=a'u, O0 (19) (0.1) = 0, (L)= u(z,0) = S()

Q: If f(x) = f'(x) = 5 t³ dt, then 4x and and f'(-2) =

A: If , then to find .

Q: If f(4)= 3 and f'(4) = –5, find g'(4) when g(x)=² (4) Your answer

A:

Q: Find the first derivative of the following functions with respect to x: a) y= Inx3 b) y = ln (÷) c)…

A: We can make it easier for you.

Q: Differentiate. h(x) = In(xe-2*)

A: First simplify the given function using properties of lograthim than simply take the derivative.

Q: Use quotient rule to find the derivative of g(x) : 2+5 22+6x Select one: O a. g'(x) = 2x3-30r-5:z?…

A:

Q: Find f'(x) and f"(x). f'(x) f"(x) = f(x) = (x³ + 7)ex

A:

Q: 2 (0) IF F(x)= x 'e', Find f'(x) and F (1)

A: Finding the derivative of the function.

Q: 7) if p(X) =- ) , and grea) =0; g'LW)=), Find f'la). %3D

A:

Q: 7) Find f(e) if a) f'(;) = { x and f6)=2 D f'(x)=\+sinx & f 3.

A: Here we find the f(x) using integration.

Q: L-'(1] (a) 8(t) (b) 1 (c) u(t) (d) Doesn't exist В D C A

A: We have to find

Q: 2x + 4 Find f'(x) if f(x) x2 + 7 f'(x) =

A:

Q: 8.. If L' { f(p)} = F (t) then L1 {f( ap) } is : a) aF(at) b) F (t/a) c) F(at) d) (1/a)F (t/a)

A:

Q: 9x Let f(x) = - 10 - Then f'(9) And after simplifying f'(x) =

A:

Q: Find f f(x) dx if 4 for a 4.

A: I=∫05fxdxif fxdx=4for x<4xfor x≥4

Q: If h'(3) = 5 and h'(1) =-1, then h"(x)dz %3D (A) -6 (B) 4 (C) 5 (D) 6

A:

Q: 7 Let f(x) = Find f'(x). (8x2 + 2x – 6)* f'(x) =

A:

Q: Q/ Find the derivative of R(z) 6 - Vz3 8z4 1 Add file

A:

Q: Let F(3) = 1, F'(3) = 5, H(3) = 2, H' (3) = 2. A. If G(2) = F(z) · H(2), then G' (3) B. If G(w) =…

A:

Q: y = (2x2 + cotx)³ P a. y' = 3(2x² + cot(x))² (4x – csc²(x O b. y' = 3(2x2 + cot(x))² (4x – cot?(x) P…

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

Q: f(z) 2+3x1x², find f'(5).

A: f(x)=2+3x−4x2, find f′(5).

Q: 4x Let f (x) Then the derivative of f is %3D 1 + 4* f'(x) = A(1 + 4*) – Bx(4*) In C where (1 + 4*)D…

A:

Q: 8.If fx)=X where gl4)=0, and a'(4)=1 then Pl2)=?

A: Given a function with data :

Q: If y = f(g(h(x))), then the derivative y/ is given by which formula? a) None of these Ob) f'(g(h(x))…

A:

Q: Suppose F(z) = g(f(z)) and f(2)= 3. f(2)=-3, g(3) = -1 and g (3)=-4. Find F(2).

A: Recall: Chain Rule  Let F(x)=g(f(x)) , then F'(x)=g'(f(x)) f'(x)

Q: 7x Let f (x) : Then the derivative of f is %3D 1 + 5* f'(x) = A(1 + 5*) – Bx(5*) In C, where (1 +…

A:

Q: a) If h(u)=-9e^(5u)^(4), then h'(u)= b) If F(x)=e^(4x^2+5x), then F'(x)=

A:

Q: Suppose h (x) =() . What is the correct result of the derivative of h with respect to x? ". In (5) A…

A: Derivative using chain rule of differentiation.

Q: Find f'(2) for f(x) 2 (x-)-

A: Given; f(x)=(x-1/x)^2 We have to find f'(2)=?

Q: What is the value of h'(1) if ha)= f(x+g«) and g(1)=1, g'(1)=1 and f(2)=3

A: A function is given by: h(x) = f(x + g(x)) We have to find h'(1) when g(1) = 1, g'(1) = 1 and f'(2)…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.