×

## 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.)

# Second Order Derivatives

Suppose that $f(x)=xe^{ax+b}, f'(0)=3, f''(0)=6,$ where $$a$$ and $$b$$ are constants. What is $$a+b?$$

What is the second derivative of $$f(x)=x^{9}e^x$$ with respect to $$x$$?

If $$\displaystyle f(x)=\frac{18}{x},$$ what is the value of $\lim_{x \to 1} \frac{f'(x)+18}{x-1}?$

What is the second derivative of $y=(x^2+2x+7)^2?$

$$f(x)=xe^{ax+\ln b}$$, where $$a$$ and $$b$$ are constants. If $$f'(0)=7$$ and $$f''(0)=126$$, what is the value of $$a+b$$?

Details and assumptions

$$\ln x$$ denotes $$\log_e x$$.

$$f''(x)$$ denotes the second derivative of $$f(x)$$.

×