Question

find all the differential equations of all tangents to y=x^2

Answer 1

The tangent at \(x_0\) is :\[
y-f(x_0) = f'(x_0) (x-x_0) \implies y = xf'(x_0)-x_0f'(x_0)+f(x_0)
\]

Answer 2

First find the derivative.

Answer 3

after that?

Answer 4

Plug in \(x_0\)

Answer 5

done

Answer 6

What is the final answer?

Answer 7

but wherz the differential equation ?>

Answer 8

y=x^2
applying d/dx on both sides
\[\frac{ d }{ dx }y=\frac{ d }{ dx }x^2\]
\[y \prime=2\times x ^{2-1}\]
\[y \prime=2x\]
\[\frac{ d }{ dx }y=2x\]

remember this formula
\[ \frac{d }{ dx }x ^{n}=nx ^{n-1}\]