Problem 2 a. If y(t) = x₁(1) * x₂(t) = e^(1+3)u(t+3), find z(t) = x₁(t+4)* x₂(t−5). b. If x₁(1) = 8e²¹u(-1) and x₂(1)=0.258(1-4), find y(t)=x,(t)* x₂(t). If x₁(1) = 4e²u(t) and x₂ (1)= u(1), find y(t) = x₁(1) * x₂ (1) C.

Q: If y = a³ + e*, find y(4) when a = 0

A: Given: y=x3+ex   As we know that; The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 And…

Q: If y = (9x + 5)x, find y'(1).

A:

Q: If h(x) = √6 +5f(x), where f(3) = 6 and f '(3) = 3, find h'(3).

A: To find the derivative of given function

Q: 6. If g(x) = x'+x²+ g"(2). find the value of

A: see 2nd step.

Q: If (g(5x) = -15, then g'(x) = %3D %3D (b) 3 (a) 0 (c)- (d) –3

A:

Q: If h(2) = 4 and h'(2) = π, find g'(2) where g(x) = 2x h(x) + cos(x)

A: To find out the derivative of the given function.

Q: Suppose F(3) = 2, F(8)= -19, and F"(x) = f(x). —13, and G'(x) = g(x). Also suppose G(3) =0, G(8) = =…

A: use integration  for finding the values.

Q: 5. If y=5x²-3x + 10, give y'(-1)

A: We have to find the y'(-1).

Q: If h(x) =/4+3f(x), where f(1) = 7, and f'(1) = 4, find the value of h'(1).

A:

Q: If y = (x+1)/(2x - root x' then y' will be?

A:

Q: Find y'

A: given

Q: Suppose the units of f(x) are square meters, when x is measured in persons. The units of f'(x) will…

A: Given, The units of fx are square meters, where x is measured in persons We have to find the units…

Q: 5. Solve the equation xydx + (x + 1)dy = 0. ex = cy(x + 1) yex = c(x + 1) c. y = cex(x + 1) d. ye*(x…

A:

Q: If g(x) = (x^2 − 1)/(2x+1) , find g′(−1).

A:

Q: If h(2) = 4 and h'(2) = -7, find d(h(x) хр x = 2.

A:

Q: If h(2) = 6 and h'(2) = −2, find d (h(x) dx X :). x = 2

A: Topic = Derivative

Q: If h(x) = V6 + 5f(x), where f(4) = 6 and f '(4) = 5, find h'(4). %3D h'(4) =

A: Given,  hx = 6+5fx ,  Where f4 = 6  and  f'4 = 5 We have to find  h'4

Q: If h(x) h'(3) = 7 + 6f(x), where f(3) = 7 and f '(3) = 2, find h'(3).

A: Write h(x) using exponent.