U₂ = k Uxx + ax (0

Q: If y = f(x), then f'(x), y', [Select] dy da and f(x) all represent the of fat x.

A: If , then to determine the meaning of .

Q: If f(x) = f'(x) = 1 x³ 3 √t² + 1 dt then F

A: Here we will use the Leibniz theorem to  find the derivative of the given problem, so on using this…

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A:

Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

A:

Q: f(z +

A:

Q: V4 + 3f(x), where f(1) = 7 and f'(1) = 4, 62. If h(x) find h'(1).

A:

Q: Compute r"(t). r(t) = + (5t³)j + (4 ln(8t))i

A:

Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

A:

Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

A:

Q: Find y'' for y = 4+ 5X 3

A: Given :   y=4+5x3     To Find : y''

Q: 5 3. Let F(x) /t2 17 dt. Find F'(x)

A: Given:

Q: If y=+*+9x²+26x+24 gấp 46 find f'(2).

A:

Q: Ex Find div F when F=3xyi+ 2xy3at (リ-1)

A: To find divergence of the given vector field at (1,-1)

Q: Let f(t) = 4t* – 4t + 5e'. Then f'(t) =

A: find the derivative

Q: Find the function F(x) such that F' (x) = 8x and F(0) = 1 O 1+4x^2 O 4x^2

A: topic- Functions

Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

A: