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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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5(9-x)/3 +1 less than 11<br>find x​
Lunna [17]

Answer:

x > \frac{1}{5}

Step-by-step explanation:

\frac{5(9-x)}{3+1}

Add 3 and 1 to get 4.

\frac{5(9-x)}{4}

Use the distributive property to multiply 5 by 9−x.

\frac{45-5x}{4}

Subtract  45/5 from both sides.

-\frac{5}{4}x

Since 44/4 and 45/4 have the same denominator, subtract them by subtracting their numerators.

-\frac{5}{4} x

Multiply both sides by -4/5, the reciprocal of -5/4. Since -5/4 is negative, the inequality direction is changed.

x>-\frac{1}{4} (-\frac{4}{5} )

Multiply -1/4 times -4/5 by multiplying numerator times numerator and denominator times denominator.

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5 0
3 years ago
Can anyone please help me with this???
ira [324]

Answer:

x=8a

Step-by-step explanation:

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add 4 to both sides

(3/a) x = 24

Divide by 3/a

x = 24 / (3/a)

Use KCF (keep change flip)

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3 0
3 years ago
Fabio has run five eighths of the race. What fraction of the race remains?
Pavel [41]

Answer:

\frac{3}{8}

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<h2><u>Fractions </u></h2>

since \frac{5}{8} has been completed

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since <em>denominators are the same </em>

= \frac{8 - 5}{8} \\\\

= \frac{3}{8}

<u>the fraction of the race that is remaining is 3/8</u>

7 0
3 years ago
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