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Implicit differentiation- Home
- Calculus 1
- Differentiation

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- Lesson: 12:17
- Lesson: 2a2:05
- Lesson: 2b2:01
- Lesson: 2c4:06
- Lesson: 2d0:48
- Lesson: 2e1:50
- Lesson: 3a7:48
- Lesson: 3b3:40
- Lesson: 4a4:08
- Lesson: 4b4:03

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 $f(x)$.

- 1.The concept of higher order derivatives
- 2.
**$1^{st}$ 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)$f(x)=5 \ln x$ - 3.
**$2^{nd}$ derivatives with implicit differentation**

Find $y"$ by implicit differentiation for the following functions:a)$x^2+y^2=9$b)$x^2+xy=9$ - 4.
**Derivatives with repeating patterns**

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

2.

Differentiation

2.1

Definition of derivative

2.2

Estimating derivatives from a table

2.3

Power rule

2.4

Slope and equation of tangent line

2.5

Chain rule

2.6

Derivative of trigonometric functions

2.7

Derivative of exponential functions

2.8

Product rule

2.9

Quotient rule

2.10

Implicit differentiation

2.11

Derivative of inverse trigonometric functions

2.12

Derivative of logarithmic functions

2.13

Higher order derivatives

We have over 170 practice questions in Calculus 1 for you to master.

Get Started Now2.1

Definition of derivative

2.3

Power rule

2.4

Slope and equation of tangent line

2.5

Chain rule

2.6

Derivative of trigonometric functions

2.7

Derivative of exponential functions

2.8

Product rule

2.9

Quotient rule

2.10

Implicit differentiation

2.11

Derivative of inverse trigonometric functions

2.12

Derivative of logarithmic functions

2.13

Higher order derivatives