Find the derivative of the function using chain rule and general power rule

`y=x sqrt(2x+3)`

chain rule=

general power rule=

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**Chain rule**

`f(g(x))'=f'(g(x))cdot g'(x)`

E.g.

`(sin(x^2))'=cos(x^2)cdot2x`

Here `f(x)=sin(x)` and `g(x)=x^2`.

**General power rule**

`(x^n)'=nx^(n-1)`

E.g.

`(x^3)'=3x^2`

We will also need **product rule**

`(f cdot g)'=f' cdot g+f cdot g'`

Let's now differentiate our function `y`.

`y'=(x sqrt(2x+3))'=`

We first use product rule.

`x'sqrt(2x+3)+x(sqrt(2x+3))'=` **(1)**

Now we use general power rule for

`x'=1`

and then we use chain rule for

`(sqrt(2x+3))'=1/2sqrt(2x+3)cdot2=1/sqrt(2x+3)`.``

Now we put that into (1) to get `y'.`

**Thus the solution is:**

`y'=sqrt(2x+3)+x/sqrt(2x+3)`

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