Mathematics 53 2nd Semester, A.Y. 2014-2015Exercises 7 - Differentiation II Q3, R3, W8, X8

I. Apply the Chain Rule to finddy

dx. There is NO need to simplify.

1. y =x2/3 secx+ 2

x2 sin3(5x)

2. y =sec2 x+ 3x2.5

6x+ 3x+

3. y =[x+ (x+ sin2 x)3

]44. y = sin4

(5 sinx

cot 2x

)5. y = cos3[ sec(tan(3x4 + 5))]

6. y =

x cosx

3x3 + tan 5x

7. y = cot

3x3 + sin 4xx3 cscx

8. y =

cos4(3x) 7x

tan(x2) 2e

9. y = csc3(

3x2 + cot 5x

e+ x+ 3

)

10. y =

3x4 2 2

cot(x2) 43x

II. Do as indicated.

1. Let f(x) =

{tan(1 x), if x > 1

x2 x, if x 1 . Determine if f is differentiable at x = 1.

2. Let f(x) =

{x2 + (1 x)4/3, if x < 1

2x2 2x, if x 1 . Determine if f is differentiable at x = 1.

3. Let f(x) =

4

1 + x+ 2, if x 1

2x3 3x2 + x, if x > 1. Determine if f is differentiable at x = 1.

4. Find the value of b so that f(x) =

b2 + 4b

4x, if 0 < x < b

1 x4, if b x

is differentiable at x = b.

5. Let f(x) =

ax2 3, if x 2

bx+ 2 +

9x

2, if x > 2

. Find the values of a and b so that f is differentiable

at x = 2.

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