The integral f(x)dx is transformed into f, 9(t)dt by applying the change of variable:

Q: d_(F(x*)) d dt dx dx 16

A: To find- solve the given equation.

Q: --1/0 -1 -1 1,0

A: As we can see  in the figure the tangent line passes through the point x=2. Slope of tangent line…

Q: Let f(t) = 3t4 - 6t+ 3et. Then f'(t) =

A: To find f'(t)

Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

Q: 2t5 + t2 – 5 h (t) = t2

A:

Q: Evaluate the function when x = 1, 3 and 3 3 1) f(x) = x + 2x - 3

A:

Q: Find the derivative of f (t) = (6t3³ - 8t² + 7) 46 f' (t) = BA

A: Given query is to find indicated derivative.

Q: Use Linear Approximation to estimate Af f (2.05)-f(2) for f(x) = %3D x+I (Use decimal notation. Give…

A:

Q: Find the derivative of the inverse of f for t = 0,

A: The derivative of a definite integral is given by the second fundamental theorem of calculus as…

Q: Ho Find (yor dy d'y ) and (y or -) for the following functions: dx dx L 2. y= x² (x-1)² 5. y=(x²…

A: We need to find the first order and 2nd order derivatives of the given functions.

Q: Determine the second derivative of 6 y – xy²= 1 -

A:

Q: (2x + 3)4 (5x + 1)(x² + 3) y = (3х — 1)3, Find the derivative of the function x3 + 4 A. dy dx (2x+3)…

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Q: Evaluate the derivative So (3t² – 2t +1) dt. -

A:

Q: g(t) = V(1 – 3t)4 + t4

A:

Q: 19 -e 8x + · -2x y = c¡e¬* + c2e¯ xe8x %3D 8100 90

A:

Q: Example If F[f(t)] =el/(1+f^2) find the F.T of F[f(2t)] 1+f2

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Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

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Q: Find the linearization of the function f (x) = a° at a = 1.

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Q: y° – 5y3 + 2y f (y) ,3

A: