Higher order derivatives

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

  1. The concept of higher order derivatives
  1. 1st1^{st} and 2nd2^{nd} derivatives.
    Find the first and second derivative for the following functions:
    1. f(x)=x4+5x2+3x+2 f(x)=x^4+5x^2+3x+2
    2. f(t)=sin(2t) f(t)=\sin (2t)
    3. g(s)=(2s+5s2)7g(s)=(2s+5s^2)^7
    4. y=5 y=5
    5. f(x)=5lnx f(x)=5 \ln x
  2. 2nd2^{nd} derivatives with implicit differentation
    Find y"y" by implicit differentiation for the following functions:
    1. x2+y2=9 x^2+y^2=9
    2. x2+xy=9 x^2+xy=9
  3. Derivatives with repeating patterns
    Find f(100)(x)f^{(100)}(x) for the following functions:
    1. f(x)=sin(x) f(x)= \sin (x)
    2. f(x)=e(2x) f(x)=e^{(2x)}
Topic Notes
If f(x)f'(x) is the derivative of f(x)f(x), then we say that f"(x)f"(x) is the 2nd2^{nd} derivative of f(x)f(x). Similarly, f(n)(x)f^{(n)}(x) is the nthn'th derivative of f(x)f(x).