# differentiation

differentiation

Name

Instruments

Subject

Date

Differentiation

1. Differentiate the following equation with respect to x:

ex2+y + ln(x) + xy2 = x

2. Calculate dy/dx for the parametric equation

x = 3t2 + e2t

3. Calculate the Tayor series of e2x/1 + 2x in powers of x - 1 up to the term in (x - 1)2.

2x/ (1 + 2x)

4. Simplify the following using partial fractions:

4x2 - x – 4/(x2 + 1)(x - 1)

5. Calculate

∫ex √ (1 + ex) dx:

6. Calculate

√(x2 - 2x - 1)e2x dx

7. Find the area between the x-axis, the lines x = -1 and x = 6, and the curve

y = x2 - x – 6

for x = -1, y = -12- (-1) – 6

8. Calculate the general solution of Yt - 2Yt -1 = 3 and describe the behaviour of the function as t tends to infinity.

Yt - 2Yt -1 = 3

9. Calculate the general solution of Yt +1/3 Yt - 1 = 3t + 2

10. Solve the equation dy/dx + 2y = x2 + 1 with y(0) = 1

Dy/dx = x2 – 2y + 1

Name

Instruments

Subject

Date

Differentiation

1. Differentiate the following equation with respect to x:

ex2+y + ln(x) + xy2 = x

2. Calculate dy/dx for the parametric equation

x = 3t2 + e2t

3. Calculate the Tayor series of e2x/1 + 2x in powers of x - 1 up to the term in (x - 1)2.

2x/ (1 + 2x)

4. Simplify the following using partial fractions:

4x2 - x – 4/(x2 + 1)(x - 1)

5. Calculate

∫ex √ (1 + ex) dx:

6. Calculate

√(x2 - 2x - 1)e2x dx

7. Find the area between the x-axis, the lines x = -1 and x = 6, and the curve

y = x2 - x – 6

for x = -1, y = -12- (-1) – 6

8. Calculate the general solution of Yt - 2Yt -1 = 3 and describe the behaviour of the function as t tends to infinity.

Yt - 2Yt -1 = 3

9. Calculate the general solution of Yt +1/3 Yt - 1 = 3t + 2

10. Solve the equation dy/dx + 2y = x2 + 1 with y(0) = 1

Dy/dx = x2 – 2y + 1

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