First slide

Diffrentiation

Question

Find $\frac{d y}{d x},$ when $y = x^{2} + 4 x^{- 1 / 2} - 3 x^{- 2}$

Moderate

A

$2 x - 2 x^{3 / 2} + 6 x^{- 3}$
B

$2 x - 2 x^{- 3 / 2} + 6 x^{- 3}$
C

$2 x - 2 x^{- 3 / 2} + 3 x^{- 3}$
D

$2 x - 2 x^{- 3 / 2} + 6 x^{- 2}$

Solution

$\frac{d y}{d x} = \frac{d}{d x} (x^{2} + 4 x^{- 1 / 2} - 3 x^{- 2}) = \frac{d}{d x} (x^{2}) + \frac{d}{d x} (4 x^{- 1 / 2}) - \frac{d}{d x} (3 x^{- 2}) = \frac{d}{d x} (x^{2}) + 4 \frac{d}{d x} (x^{- 1 / 2}) - 3 \frac{d}{d x} (x^{- 2}) = 2 x - \frac{1}{2} (4) x^{- 3 / 2} - 3 (- 2) x^{- 3} = 2 x - 2 x^{- 3 / 2} + 6 x^{- 3}$

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