# What is the equation of the line tangent to #f(x)=x ^2cos2x # at #x=pi/4#?

##### 1 Answer

#### Explanation:

**We will first find the derivative of #f(x)#.**

**By product rule, this will become:**

**By power rule, #d/dx(x^2)# becomes #2x^1#.**

**The derivative of #cosx# is #-sinx#. But since we are getting the derivative of #cos2x# instead, we need to use chain rule.**

**The derivative of #2x# is simply #2#.**

**Now that we have the derivative of #f(x)#, we can solve for the slope of the tangent line at #x=pi/4#.**

**We now look for the point of #f(x)# at #x=pi/4#.**

**Finally, we can solve for the equation of the tangent line.**