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Artemon [7]
3 years ago
8

Differenciate x^6 with respect to 1/√x

Mathematics
1 answer:
hoa [83]3 years ago
7 0
DIFFERENTIATION \\ \\ \\ Let \: u \: = \: {x}^{6} \: \: \: and \: v = \frac{1}{ \sqrt{x} } \\ \\ Then \: , \: \frac{du}{dx} \: = \: 6 {x}^{5} \\ \\ and \: \: \: \: \: \: \frac{dv}{dx} \: \: = \: \frac{ - 1}{2x \sqrt{x} } \\ \\ \\ Therefore \: , \\ \\ \\ \frac{du}{dv} \: = \: \frac{ \frac{du}{dx} }{ \frac{dv}{dx} } \: = \: \frac{6 {x}^{5} }{ \frac{ - 1}{2x \sqrt{x} } } \\ \\ \frac{du}{dv} \: = \: \frac{ \frac{du}{dx} }{ \frac{dv}{dx} } \: = - 12 {x}^{ \frac{13}{2} } \\ \\ \\ \frac{du}{dv} \: = - 12 {x}^{ \frac{13}{2} } \: \: \: \: \: \: \: \: Ans.
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substitute each coordinate point into the left side of the equation and if equal to 21 then it is a solution.

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(11 , 3) → (3 × 11 )  - ( 4 × 3) = 33 - 12 = 21

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substitute the coordinates into the equation and if equal to 13 the it is the solution.

(2 , - 9 ) → (5 × 2 ) - (-9)/3 = 10 + 9/3 = 10 + 3 = 13

(3 , - 6) → (5 × 3) - (- 6)/3 = 15 + 6/3 = 15 + 2 = 17

thus (2 , -9 ) is the solution

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multiply both sides by 3

x = 3 × - 15 = - 45

thus x -intercept = ( - 45 , 0)



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Step-by-step explanation:

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