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Implicit differentiation- Home
- AP Calculus BC
- Derivatives

Still Confused?

Try reviewing these fundamentals first.

Calculus

Power ruleCalculus

Chain ruleCalculus

Derivative of exponential functionsCalculus

Implicit differentiationStill Confused?

Try reviewing these fundamentals first.

Calculus

Power ruleCalculus

Chain ruleCalculus

Derivative of exponential functionsCalculus

Implicit differentiationNope, I got it.

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Get Started Now- Intro Lesson2:17
- Lesson: 1a2:05
- Lesson: 1b2:01
- Lesson: 1c14:14
- Lesson: 1d0:48
- Lesson: 1e1:50
- Lesson: 2a7:48
- Lesson: 2b3:40
- Lesson: 3a4:08
- Lesson: 3b4:03

Basic concepts: Power rule, Chain rule, Derivative of exponential functions, Implicit differentiation,

Note

If $f'(x)$ is the derivative of $f(x)$, then we say that $f"(x)$ is the $2^{nd}$ derivative of $f(x)$. Similarly, $f^{(n)}(x)$ is the $n'th$ derivative of $f(x)$.

If $f'(x)$ is the derivative of $f(x)$, then we say that $f"(x)$ is the $2^{nd}$ derivative of $f(x)$. Similarly, $f^{(n)}(x)$ is the $n'th$ derivative of $f(x)$.

- IntroductionThe concept of higher order derivatives
- 1.
**$1^{st}$ and $2^{nd}$ derivatives.**

Find the first and second derivative for the following functions:

a)$f(x)=x^4+5x^2+3x+2$b)$f(t)=\sin (2t)$c)$g(s)=(2s+5s^2)^7$d)$y=5$e)$f(x)=5 \ln x$ - 2.
**$2^{nd}$ derivatives with implicit differentation**

Find $y"$ by implicit differentiation for the following functions:a)$x^2+y^2=9$b)$x^2+xy=9$ - 3.
**Derivatives with repeating patterns**

Find $f^{(100)}(x)$ for the following functions:a)$f(x)= \sin (x)$b)$f(x)=e^{(2x)}$

2.

Derivatives

2.1

Definition of derivative

2.2

Estimating derivatives from a table

2.3

Power rule

2.4

Chain rule

2.5

Derivative of trigonometric functions

2.6

Derivative of exponential functions

2.7

Derivative of logarithmic functions

2.8

Product rule

2.9

Quotient rule

2.10

Derivative of inverse trigonometric functions

2.11

Implicit differentiation

2.12

Higher order derivatives

We have over 320 practice questions in AP Calculus BC for you to master.

Get Started Now2.1

Definition of derivative

2.3

Power rule

2.4

Chain rule

2.5

Derivative of trigonometric functions

2.6

Derivative of exponential functions

2.7

Derivative of logarithmic functions

2.8

Product rule

2.9

Quotient rule

2.10

Derivative of inverse trigonometric functions

2.11

Implicit differentiation

2.12

Higher order derivatives