How do I differentiate sin 2 x?I thought that because this is true: sin...
How do I differentiate ?
I thought that because this is true:
I could differentiate the expression like this:
But I am supposed to get
Why am I wrong?
Answer & Explanation
You can only use the rule: if x is just x and not a function. In the case for then as you write it in the form you can see that we can't use the power rule because it's not just an x term being raised to a constant power, it's a function being raised to a constant power. To differentiate one must use the Chain Rule because is a function of x within another function (the function that is squaring ) . The chain rule is: so you can apply that rule for this case with and
You are using the chain rule incorrectly:
Now and , therefore
And to explain your other point of confusion: is a well-known trigonometric formula