# How do you differentiate #g(x) =x^2tanx# using the product rule?

##### 2 Answers

#### Explanation:

The product rule states that the derivative of

We solve these problems by first finding the derivatives of each piece. In this case, we have

Now we substitute

We could rewrite this in other ways, like

g'(x) =

# x^2sec^2x + 2xtanx #

#### Explanation:

using the product rule :

If g(x) = f(x).h(x) then g'(x) = f(x).h'(x) + h(x).f'(x)

here let f(x)

#=x^2color(black)(" and ") h(x)= tanx # hence g'(x)

# = x^2 d/dx(tanx) + tanx d/dx(x^2) #

# = x^2 (sec^2x) + tanx(2x) = x^2sec^2x + 2xtanx #