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## Higher-order Derivatives

The first derivative is the slope of a curve, and the second derivative is the slope of the slope, like acceleration. So what's the third derivative? (Fun fact: it's actually called jerk.)

# 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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