Calculus

# Third and 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 $f'''(0)?$

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