# How do you differentiate #g(x) =x^3 sqrt(4-x)# using the product rule?

##### 3 Answers

#### Answer:

#### Explanation:

#"Given "y=f(x)h(x)" then"#

#dy/dx=f(x)h'(x)+h(x)f'(x)larrcolor(blue)"product rule"#

#f(x)=x^3rArrf'(x)=3x^2#

#h(x)=sqrt(4-x)=(4-x)^(1/2)#

#"differentiate using the "color(blue)"chain rule"#

#rArrh'(x)=1/2(4-x)^(-1/2)xxd/dx(4-x)#

#color(white)(rArrh'(x))=-1/(2sqrt(4-x))#

#rArrg'(x)=-(x^3)/(2sqrt(4-x))+3x^2sqrt(4-x)#

#### Answer:

#### Explanation:

We are given:

We apply the product rule as follows:

Simplifying:

#### Answer:

#### Explanation:

We can use the product rule with the form;

Where we let one term equal to

Here;

Let

And we can do the same for

Let

Just like

By using chain rule;

Now we can substitute these equations in blue into the equation from the start;