Question

Differentiation w.r.t x
Root x (x^2+7)

Answer 1

Answer:

$y = \sqrt{x} ( {x}^{2} + 7) \\ \frac{dy}{dx} = \sqrt{x} \times \frac{d}{dx} ( {x}^{2} + 7) + ( {x}^{2} + 7) \times \frac{d}{dx} ( \sqrt{x} ) \\ = \sqrt{x} \times (2x + 0) + ( {x}^{2} + 7) \times \frac{1}{2 \sqrt{x} } \\ = 2x \sqrt{x} + \frac{( {x}^{2} + 7) }{2 \sqrt{x} } \\ = \frac{4 {x}^{2} + {x}^{2} + 7 }{2 \sqrt{x} } \\ = \frac{5 {x}^{2} + 7}{2 \sqrt{x} } ans$