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Implicit differentiation- Home
- UK Year 13 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)$f(x)=e^{(2x)}$

24.

Derivatives

24.1

Definition of derivative

24.2

Power rule

24.3

Slope and equation of tangent line

24.4

Chain rule

24.5

Derivative of trigonometric functions

24.6

Derivative of exponential functions

24.7

Product rule

24.8

Quotient rule

24.9

Implicit differentiation

24.10

Derivative of inverse trigonometric functions

24.11

Derivative of logarithmic functions

24.12

Higher order derivatives

24.13

Tangent and concavity of parametric equations

We have over 760 practice questions in UK Year 13 Maths for you to master.

Get Started Now24.1

Definition of derivative

24.2

Power rule

24.3

Slope and equation of tangent line

24.4

Chain rule

24.5

Derivative of trigonometric functions

24.6

Derivative of exponential functions

24.7

Product rule

24.8

Quotient rule

24.9

Implicit differentiation

24.10

Derivative of inverse trigonometric functions

24.11

Derivative of logarithmic functions

24.12

Higher order derivatives