All categories

3 years ago

How do we know that the derivative of 1/x is equal to -1/x^2 ?

Mathematics

1 answer:

snow_lady [41]3 years ago

4 0

Answer:the derivative of 1/x =-1/x^2

Step-by-step explanation:

1/x can also be written as x^-1

Therefore d/dx of x^-1

=-1*x^-1-1

=-1x^-2

Which can also be written as -1/x^2

Note: d/dx also means derivative of x

And d/dx (a/x^b) =(a*-b) /x^(b+1)

Where a and b represents a variable

You might be interested in

FINDING AREA ON A COORDINATE PLANE

Fynjy0 [20]

Answer:

This is not descriptive at all..?

Step-by-step explanation:

We need a real question.

8 0

3 years ago

Connor bought some pears.He used 2/6 of the pears to make dessert.He gave 1/4 of the remainder to his neighbor.What fraction of

Xelga [282]

1/6 portion of pears to the neighbor

3 0

4 years ago

2. Determine the sum of the first 400 ODD numbers.<br><br>

il63 [147K]

Odd numbers take the form $2n-1$ , where $n\ge1$ is an integer. When $n=400$ , the last odd number would be 799. So we're adding

$S=1+3+5+\cdots+795+797+799$

By reversing the order of terms, we have

$S=799+797+795+\cdots+5+3+1$

and we can pair up terms in both sums at the same position to write

$2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)$

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

$2S=400\cdot800\implies S=160,000$

###

We could also make use of the formulas,

$\displaystyle\sum_{i=1}^n1=n$

$\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2$

We have

$S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000$

3 0

4 years ago

Find two consecutive integers such that the larger is nine more than twice the smaller

Mars2501 [29]

If x is one integer and x+1 is the next, we have 2*x+9=x+1. Subtracting 9 and x from both sides, we get x(the smaller number)=-8 and the larger number is -7.

7 0

3 years ago

Slope for the line perpendicular to the line shown in the graph

Flauer [41]

It would be positive 1/3 because if you move to the right one on your bottom point and up 3 it gives you +1/3

8 0

3 years ago