Question

please give me right and correct answers
FIND THE DERIVATES OF THE FOLLOWING USING DEFIANTION ​

Answer 1

Answer:

The answers are (i) . $10x$ and (iii) . $\frac{1}{2\sqrt{x+1}}$

Step-by-step explanation:

(i) . $\frac{d}{dx}(5x^2-3)=5\frac{d}{dx}(x^2)-\frac{d}{dx}(3)=5(2x)-0=10x$

Using  $\frac{d}{dx}(x^n)=nx^{n-1}$ and derivative any constant is zero

(iii) . $\frac{d}{dx}\sqrt{x+1}=\frac{d(x+1)^{\frac{1}{2}}}{d(x+1)}\times \frac{d(x+1)}{dx}$, chain rule

                      $=\frac{1}{2}(x+1)^{\frac{1}{2}-1}(\frac{d}{dx}(x)+\frac{d}{dx}(1))\\=\frac{1}{2}(x+1)^{-\frac{1}{2}}(1+0)\\=\frac{1}{2}\times \frac{1}{(x+1)^{\frac{1}{2}}}=\frac{1}{2\sqrt{x+1}}$