Question

if y=x^3+1/x^3+9 calculate dy/dx​

Answer 1

Answer:

dx³+1/x³+9/dx = 3x² - 3x⁻⁴

Explanation:

y=x³+1/x³+9

 =x³+x⁻³+9

dx³/dx = 3x² [dxⁿ/dx = nxⁿ⁻¹]

dx⁻³/dx = -3x⁻⁴ [dxⁿ/dx = nxⁿ⁻¹]

d9/dx = 0 [Differentiation of constant is always 0]

dx³+1/x³+9/dx = 3x² - 3x⁻⁴+0

Answer 2

Answer:

$\\ \frac{dy}{dx} = 3 {x}^{2} - \frac{3}{({x}^{ 4})}$

Explanation:

$we \: \: know \: \: that \: \: \\ \\ \frac{d {x}^{n} }{dx} = n {x}^{n - 1} \\ \\ \: \: therefore \: \: we \: \: can \: \: write \: \: the \: \\ \: equation \: \: as \\ \\ y = {x}^{3} + {x}^{ - 3} + 9 \\ \\ so \\ \\ \frac{dy}{dx} = 3 {x}^{2} + ( - 3) {x}^{ - 4} + 0 \\ \\ (derivative \: of \: constant \: is \: 0) \\ \\ \frac{dy}{dx} = 3 {x}^{2} - \frac{3}{ ({x}^{4} )}$

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