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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tiburtius | High School Teacher | (Level 2) Educator

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Chain rule

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



Here `f(x)=sin(x)`  and `g(x)=x^2`.

General power rule




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


and then we use chain rule for


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

Thus the solution is: