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Calculus

Power ruleCalculus

Chain ruleCalculus

Derivative of exponential functionsCalculus

Implicit differentiation- Home
- AU Maths Extension 1
- 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)$f(x)=e^{(2x)}$

41.

Derivatives

41.1

Definition of derivative

41.2

Power rule

41.3

Slope and equation of tangent line

41.4

Chain rule

41.5

Derivative of trigonometric functions

41.6

Derivative of exponential functions

41.7

Product rule

41.8

Quotient rule

41.9

Derivative of inverse trigonometric functions

41.10

Derivative of logarithmic functions

41.11

Higher order derivatives

We have over 1640 practice questions in AU Maths Extension 1 for you to master.

Get Started Now41.1

Definition of derivative

41.2

Power rule

41.3

Slope and equation of tangent line

41.4

Chain rule

41.5

Derivative of trigonometric functions

41.6

Derivative of exponential functions

41.7

Product rule

41.8

Quotient rule

41.9

Derivative of inverse trigonometric functions

41.10

Derivative of logarithmic functions

41.11

Higher order derivatives