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Implicit differentiation- Home
- Sixth Year 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)$f(x)=e^{(2x)}$

25.

Derivatives

25.1

Definition of derivative

25.2

Power rule

25.3

Gradient and equation of tangent line

25.4

Chain rule

25.5

Derivative of trigonometric functions

25.6

Derivative of exponential functions

25.7

Product rule

25.8

Quotient rule

25.9

Implicit differentiation

25.10

Derivative of inverse trigonometric functions

25.11

Derivative of logarithmic functions

25.12

Higher order derivatives

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now25.1

Definition of derivative

25.2

Power rule

25.3

Gradient and equation of tangent line

25.4

Chain rule

25.5

Derivative of trigonometric functions

25.6

Derivative of exponential functions

25.7

Product rule

25.8

Quotient rule

25.9

Implicit differentiation

25.10

Derivative of inverse trigonometric functions

25.11

Derivative of logarithmic functions

25.12

Higher order derivatives