Chain Rule and Transcendental Functions

[Euler]

I am having some trouble differentiating the following equation

\(\displaystyle \frac{d}{dx}cos^47x\)

The answer reads

\(\displaystyle -28cos^37xsin7x\)

What I did was differentiate \(\displaystyle (cos)^4\) to get \(\displaystyle 4cos^3\), and then I differentiated \(\displaystyle cos7x\) and got \(\displaystyle -sin7x\)

Multiplying the two together I got \(\displaystyle -4cos^3sin7x\)

What'd I do wrong?

 

[tkhunny]

So close. You missed one level.

\(\displaystyle \frac{d}{dx}cos(7x)\,=\,-sin(7x)*7\)

 

[Euler]

Ah okay, and I also forgot to include 7x in my first differentiation. Thanks for that!