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How do I integrate and differentiate 1/(x^2)?

1/(x²) can be written as x^-2

We know that to differentiate you need to multiply by the value of the old power and minus 1 from it. This means dy/dx of y=...

Answered by Judy G. • Maths tutor

4028 Views

Let w, z be complex numbers. Show that |wz|=|w||z|, and using the fact that x=|x|e^{arg(x)i}, show further that arg(wz)=arg(w)+arg(z) where |.| is the absolute value and arg(.) is the angle (in polar coordinates). Hence, find all solutions to x^n=1 .
Put w=a+bi, z=c+di where a, b, c, d are real, and i²=-1. Then |wz|²=|(a+bi)(c+di)|²=|ac-bd+(ad+cb)i|²=(ac)²+(bd)²-2bcd+(ad)²+(c...
JK
Answered by Jihoon K. • Maths tutor
7752 Views

Express 9^(3x+)1 in the form 3^y giving y in the form of ax+b where a and b are constants.
Fistly show that: 9^3x+1=3^y

To find x we need to get the left hand side of the equation to be 3^m(3x+1)where 3^m
JG
Answered by Judy G. • Maths tutor
5739 Views
What is the Product Rule?
The product rule is used when differentiating two functions that are multiplied by eachother. The formula for the product rule is:

U (dv/dx) + V (du/dx) where 'dv/dx' is the differential of the...
AW
Answered by Abbie W. • Maths tutor
3661 Views
A curve has parametric equations x=t(t-1), y=4t/(1-t). The point S on the curve has parameter t=-1. Show that the tangent to the curve at S has equation x+3y+4=0.
To anwser this question we need to find a linear equation of the form y=mx+c which we can rearrange to give the desired equation. Firstly, we must find the gradient at the point S given by dy/dx. Using th...
MF
Answered by Marcus F. • Maths tutor
8017 Views
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How do I integrate and differentiate 1/(x^2)?

Let w, z be complex numbers. Show that |wz|=|w||z|, and using the fact that x=|x|e^{arg(x)i}, show further that arg(wz)=arg(w)+arg(z) where |.| is the absolute value and arg(.) is the angle (in polar coordinates). Hence, find all solutions to x^n=1 .

Express 9^(3x+)1 in the form 3^y giving y in the form of ax+b where a and b are constants.

What is the Product Rule?

A curve has parametric equations x=t(t-1), y=4t/(1-t). The point S on the curve has parameter t=-1. Show that the tangent to the curve at S has equation x+3y+4=0.

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