2 years ago

Use the quotient rule to prove that the power rule is valid for negative whole number powers.

Mathematics

1 answer:

-BARSIC- [3]2 years ago

6 0

Answer:

ddx(x−m)=−mx−m−1

That is, ddx(x−m)=−mx−m−1. where m is a positive integer.

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zubka84 [21]

Answer:

See Explanation Below

Step-by-step explanation:

Given

$(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.$

Required

Prove

To start with; we open the bracket on the left hand side

$(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)$

$(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)$

$(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x$

$(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x$

Reorder

$(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x$

From trigonometry;

$sin^2x + cos^2x = 1$

So;

$(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x$

becomes

$(sin x - cos x)^2 = 1 - 2sinx cos x$

Also from trigonometry;

$sec^2x - tan^2x = 1$

So,

$(sin x - cos x)^2 = 1 - 2sinx cos x$

becomes

$(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x$

Proved

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2 years ago

In a scale drawing, a wall is 1 1 2 inches long. The actual wall is 12 feet long. Find the scale of the drawing.

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Answer:

It is 6.59

Step-by-step explanation:

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3 years ago

Factor the expression below:<br><br> 17x –34

abruzzese [7]

Answer:

Step-by-step explanation:

17(x-2)

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Mike makes and sells skateboards. If he has a cost of $6,200 per year plus a cost of $15 per skateboard, how many skateboards mu

Roman55 [17]

Answer: 310

Step-by-step explanation:

35-15= 20

6200 / 20 = 310

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2 years ago

Use the quotient rule to prove that the power rule is valid for negative whole number powers.​

Use the quotient rule to prove that the power rule is valid for negative whole number powers.