Chapter 2 - Derivatives - Review - True-False Quiz - Page 196: 15

TRUE

Given: $f(x)=(x^{6}-x^{4})^{5}$ If this were multiplied out, the highest power term would be $(x^{6})^{5}=x^{30}$ The derivative of this term would be $f'(x)=30x^{29}...$ $f''(x)=30.29x^{28}...$ $f'''(x)=30.29.28x^{27}...$ so on $f^{30}(x)=30!x^{0}=30!$ and the derivative of a constant is $0$, so $f^{31}(x)=0$ Hence, the given statement is true.