Why is the notation startfraction dy over dx endfraction used to represent the derivative?
1 answer:
We know expression is used for represent the derivative.
Actually, derivative is the second name of " Rate of Change".
And if we read , it represents the "Rate of change of y with respect to x".
In simple words, a derivative is the rate of change or slope of a very small portion of a function.
dy represents very small change in y-coordinate and dx represents very small change in x-coordinate.
Because deriviate is the second name of " a very small rate of change".
We use to represent the derivative.
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Answer:
second option
Step-by-step explanation:
Given
+ 6x² + 5 = 0
let u = x², then
u² + 6u + 5 = 0 ← in standard form
(u + 1)(u + 5) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 1 = 0 ⇒ u = - 1
u + 5 = 0 ⇒ u = - 5
Change u back into terms of x, that is
x² = - 1 ( take the square root of both sides )
x = ± = ± i ( noting that
= i ), and
x² = - 5 ( take the square root of both sides )
x = ± = ±
= ±
×
= ± i
Solutions are x = ± i and x = ± i