Question

differentiate and intigrate √x​

Answer 1

Answer:

Step-by-step explanation:

differentiation of x^n=n.x^n-1

$\sqrt{x}=$x^1/2

dx^1/2/dx=1/2.x^-1/2

integration formula=x^n+1/n+1

n=1/2

x^1/2+1/3/2=x^3/2/3/2

Answer 2

differentiate √x with respect

to x :-

formula use

$\implies \pink { \frac{d}{dx}x {}^{n} = nx {}^{n - 1} }$

$\implies \: \frac{d}{dx} \sqrt{x} \\ \\ \implies \: \frac{d}{dx}x {}^{ \frac{1}{2} } \\ \\ \implies \: \frac{1}{2} {x}^{ \frac{1}{2} - 1} \\ \\ \implies \: \frac{1}{2} x {}^{ - \frac{1}{2} } \\ \\ \implies \: \frac{1}{2x {}^{ \frac{1}{2} } } \\ \\ \implies \: \frac{1}{2 \sqrt{x} }$

intigration √x

formula use

$\implies \int\pink{x {}^{n}dx = \frac{x {}^{n + 1} }{n + 1} }$

$\implies \int \: \sqrt{x} \: dx \\ \\ \implies \int \: x {}^{ \frac{1}{2} } dx \\ \\ \implies \: \frac{x {}^{ \frac{1}{2} + 1} }{ \frac{1}{2} + 1 } \\ \\ \implies \: \frac{x {}^{ \frac{3}{2} } }{ \frac{3}{2} } \\ \\ \implies \: \frac{2}{3} x {}^{ \frac{3}{2} }$

______________________

I hope it helps you