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Implicit differentiation- Home
- AU Year 11 Maths
- 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

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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)$f(x)=e^{(2x)}$

31.

Derivatives

31.1

Definition of derivative

31.2

Power rule

31.3

Gradient and equation of tangent line

31.4

Chain rule

31.5

Derivative of trigonometric functions

31.6

Derivative of exponential functions

31.7

Product rule

31.8

Quotient rule

31.9

Implicit differentiation

31.10

Derivative of inverse trigonometric functions

31.11

Derivative of logarithmic functions

31.12

Higher order derivatives

31.13

Position velocity acceleration

We have over 1140 practice questions in AU Year 11 Maths for you to master.

Get Started Now31.1

Definition of derivative

31.2

Power rule

31.3

Gradient and equation of tangent line

31.4

Chain rule

31.5

Derivative of trigonometric functions

31.6

Derivative of exponential functions

31.7

Product rule

31.8

Quotient rule

31.9

Implicit differentiation

31.10

Derivative of inverse trigonometric functions

31.11

Derivative of logarithmic functions

31.12

Higher order derivatives

31.13

Position velocity acceleration