write about data base system I want subheanding in that
Answers
Answer:
heading: data base system and it's uses
A database is an organized collection of data, generally stored and accessed electronically from a computer system. ... The database management system (DBMS) is the software that interacts with end users, applications, and the database itself to capture and analyze the data.
We discussed four main types of databases: text databases, desktop database programs, relational database management systems (RDMS), and NoSQL and object-oriented databases. We also talked about two ways to categorize databases based on their logical design: operational databases and database warehouses.
Uses for database systems include: They store data and provide facilities of searching specific record in given data. They store special information used to manage the data.
Answer:
solution
Let
\begin{lgathered}y \: = {tan}^{ - 1} \frac{ \sqrt{x} - 1 }{1 + {x}^{ \frac{3}{2} } } \\ \\ \rightarrow \: y = {tan}^{ - 1} \frac{ \sqrt{x} - 1}{1 + \sqrt{x} .x} \\ \\ \rightarrow \: y = {tan}^{ - 1} \sqrt{x} - {tan}^{ - 1} x\end{lgathered}
y=tan
−1
1+x
2
3
x
−1
→y=tan
−1
1+
x
.x
x
−1
→y=tan
−1
x
−tan
−1
x
Now , Differentiate w.r.t. x we get ,
\begin{lgathered}\frac{dy}{dx} = \frac{d}{dx} ( {tan}^{ - 1} \sqrt{x} - {tan}^{ - 1} x) \\ \\ \implies \: \frac{dy}{dx} = \frac{1}{1 + x} . \frac{1}{2 \sqrt{x} } - \frac{1}{1 + {x}^{2} }\end{lgathered}
dx
dy
=
dx
d
(tan
−1
x
−tan
−1
x)
⟹
dx
dy
=
1+x
1
.
2
x
1
−
1+x
2
1
Formula used :
\bold{\frac{d}{dx} {tan }^{ - 1} = \frac{1}{1 + {x}^{2} } }
dx
d
tan
−1
=
1+x
2
1
\bold{ \frac{d}{dx} \sqrt{x} = \frac{1}{2 \sqrt{x} } }
dx
d
x
=
2
x
1