find all functions u(t) that solve the equation u'(t)+t*u(t)=-t * e^(-t^2), subject to u(0) = 1

Q: Find f'(z) of f(z) = e(z^3) - 5z.

A: Given :- f(z) = e(z^3) - 5z

Q: find y as a function of x if: y'''-13y''+42y'=60e^x, y(0)=11, y'(0)=24, y''(0)=21

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Q: Find f(x) if f "(x) = x -3/2, f ' (4) = 1  and f(4) = 4.

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Q: Now, differentiate the function y' = 4x(1 + 2 In). y" = 4 + 8 + In + 8 In

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Q: 3. f(t) = -2t2 + 3t – 6 6. h(s) = s4/5 1 +1 9. h(t) = 1* + 21 + 2

A: To find the derivative of f(t)=-2t2+3t-6, use the power rule of differentiation, ddttn=ntn-1.

Q: If f(x) = 3/7(2 – 7a + 5), find f'(x). - Find f'(3).

A: Given:- f(x) = 3√x(x3-7√x+5)  To find:- f'(x) and f'(3)

Q: Find f'(x) for the function. RM) = 7x(17x* + ) x + 1 f'(x) = %3D

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Q: Find  f'(a)

A: Here given function as ft=2t+1t+3

Q: Differentiate. G(x) = (8x² + 9) (4x + Vx) Gʻ(x) =D %3D

A: We know that, from product rule of differentiation ddxfx·gx=fx·g'x+gx·f'x                  ⋯⋯1 We…

Q: Find y=f(x) if f''(x)=4x^2, f'(0)=3, and f(0)=2.

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Q: Find h(t) if h"(t)=t^(3/2), h'(4)=2 and h(0) = 3.

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Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

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Q: 2x+1 (b) g(x) = f(x)

A: We want to find the differential of g(x)

Q: Compute the first four derivatives of h(t)=9t2−2et h(t)=9t^2−2e^t. a) h′(t)=   b) h′′(t)=   c)…

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

A: Using Quotient Rule of Derivatives

Q: (ii) Show that {Xt} is stationary.

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Q: Find the second derivative of the function f(t)= t³sect. Of"(t)= t³sect(20+tsect+10ttant+ftan²t)…

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