deriatives for test review

Question

Answer 1

2)

a)

d/dx (2x³ - x^3/2 + (4/√x))

= d/dx (2x³ - x^3/2 + (4x^-1/2)

=2d/dx (x³) - d/dx (x^3/2)+4 d/dx(x^-1/2)

=2(3x²) - (3/2)(x^3/2-1)+4 (-1/2) d/dx(x^-1/2-1)

=6x² - (3/2)(x^1/2) - 2 x^-3/2

Answer 2

2)

c)

Apply formula  :

 

Comments

apply the formula, please explain how you get from step 2 to 3. where tje 3 and 1 come from

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Explaination from step 2 to 3 :

Here Consider

U = 3x - 4

V = x + 2

Then substitute in formula :

Substitute U = 3x - 4 and V = x + 2

Explaination of 3 and 1 come from :

Answer 3

2)

b)

Apply formula a^maⁿ = a^m+n

Apply formula  : (d/dx) (xⁿ) = nx^n-1

3(5/2)x^(5/2)-1 - (3/2)(-3/2)x^(-3/2)-1

(15/2)x^(3/2) + (9/4)x^(-5/2)

The solution is (15/2)x^(3/2) + (9/4)x^(-5/2)