Calculus
Higher-order Derivatives
For the function \[f(x)=e^x(7\sin x+3\cos x),\] what is the third derivative \( f'''(x)\)?
What is the \(19 ^{th}\) derivative of \(\displaystyle \frac{1}{3}e^{3x}?\)
If \(f(x)=2x^4-15x^3+15x-17,\) what is the value of \(\displaystyle \lim_{x \to 1} \frac{f''(x)+66}{x-1}?\)
What is the third derivative of the function \(y=8\sin x\) with respect to \(x\)?
If \(f(x)=e^{5x},\) what is the value of \(f'''(0)?\)