Differentiation

Question 1. $~3x^{4/3}~-~2x^{-2}~$ choose correct answer below:

$~(9/7)x^{7/3}~+~2x^{-1}~$

$~~3x^{4/3}~+4x^{-3}~~$

$~~4x^{1/3}+4x^{-3}~$

$~~(9/4)x^{1/3}+x^{-3}~$

Question 2. $~7x^2+3x^3+4~$ choose correct answer below:

$~(7/3)x^3+(3/4)x^4+4x~$

$~14x+9x^{2}~$

$~14x+6x^{2}~$

$~7x+3x^2~$

Question 3. $~\sqrt{x^4}~+~{3\over\sqrt{2x}}~$ choose correct answer below:

$~4\sqrt{x^3}-{3\over~2\sqrt{2}}~x^{-3/2}~$

$~2x+{3\over~2\sqrt{2}}~x^{-3/2}~$

$~2x-{3\over~2\sqrt{2}}~x^{-1/2}~$

$~2x-{3\over~2\sqrt{2}}~x^{-3/2}~$

Question 4. $~(x+2)^4~$ choose correct answer below:

$~4x^3+24x^2+48x+32~$

$~4x^3+24x^2+36x+32~$

$~(1/5)(x+2)^5~$

$~8(x+2)^3~$

Question 5. Find the gradient of the curve $~y=x^4+2x^3-2/x~$ at the point where x=1.

Question 6. Find the x values of all stationary points on the curve $~y=4x^3+3x^2-6x-1~$ . Hint: there is more than one!

-2

-3/2

-1

-1/2

1/2

3/2

Question 6a. Which of the stationary points found above is a minimum?

-2

-3/2

-1

-1/2

1/2

3/2

Question 7. $~(x^2-1)\sqrt{2x-5}~$ at x=7

Question 8. $~\log\,(x^2+1)~$ at x=1

Question 9. $~\sin^2(2\pi\!x)~$ at x=1.

Question 10. $~{1-x\over~1+x}~$ at x=1.

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Mathematics Institute

Differentiation

Score 8 or more out of 11 to pass.

Section A: Differentiate the following expressions with respect to x.

Section B:

Section C: Find the derivatives of the following functions at the indicated point.

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