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MT112 - Week 6 - Lecture#02

The document discusses derivatives of explicit and implicit functions, logarithmic functions, and trigonometric functions. It provides the derivatives of sine, cosine, tangent, cotangent, secant, and cosecant functions.

Uploaded by

Muhammad Azeem
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75 views23 pages

MT112 - Week 6 - Lecture#02

The document discusses derivatives of explicit and implicit functions, logarithmic functions, and trigonometric functions. It provides the derivatives of sine, cosine, tangent, cotangent, secant, and cosecant functions.

Uploaded by

Muhammad Azeem
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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MT112

Calculus - I
Week#06
Lecture#02
Derivative of Explicit and Implicit Functions
Derivative of Explicit and Implicit Functions
Implicit Differentiation
Implicit Differentiation
Implicit Differentiation
Implicit Differentiation
Implicit Differentiation
Implicit Differentiation
Derivative of Logarithmic Functions
Derivative of Logarithmic Functions
Derivative of Logarithmic Functions
Derivative of Logarithmic Functions
Derivative of Logarithmic Functions
Derivative of Logarithmic Functions
Derivative of Logarithmic Functions
Derivative of Trigonometric Functions
𝒅
1. 𝒅𝒙
𝒔𝒊𝒏𝒙 = 𝒄𝒐𝒔𝒙

𝒅
2. 𝒅𝒙
𝒄𝒐𝒔𝒙 − −𝒔𝒊𝒏𝒙

𝒅
3. 𝒕𝒂𝒏𝒙 = 𝐬𝐞𝐜 𝟐 𝒙
𝒅𝒙

𝒅
4. 𝒅𝒙
𝒔𝒆𝒄 = 𝒔𝒆𝒄𝒙 𝒕𝒂𝒏𝒙

𝒅
5. 𝒅𝒙
𝒄𝒔𝒄𝒙 = −𝒄𝒔𝒄𝒙 𝒄𝒐𝒕𝒙

𝒅
6. 𝒄𝒐𝒕𝒙 = −𝒄𝐬𝐜 𝟐 𝒙
𝒅𝒙
Derivative of Trigonometric Functions
𝒅
1. 𝒅𝒙
𝒔𝒊𝒏𝒙 = 𝒄𝒐𝒔𝒙

𝒅
2. 𝒅𝒙
𝒄𝒐𝒔𝒙 − −𝒔𝒊𝒏𝒙

𝒅
3. 𝒕𝒂𝒏𝒙 = 𝐬𝐞𝐜 𝟐 𝒙
𝒅𝒙

𝒅
4. 𝒅𝒙
𝒔𝒆𝒄 = 𝒔𝒆𝒄𝒙 𝒕𝒂𝒏𝒙

𝒅
5. 𝒅𝒙
𝒄𝒔𝒄𝒙 = −𝒄𝒔𝒄𝒙 𝒄𝒐𝒕𝒙

𝒅
6. 𝒄𝒐𝒕𝒙 = −𝒄𝐬𝐜 𝟐 𝒙
𝒅𝒙
Derivative of Trigonometric Functions
𝒅
1. 𝒅𝒙
𝒔𝒊𝒏𝒙 = 𝒄𝒐𝒔𝒙

𝒅
2. 𝒅𝒙
𝒄𝒐𝒔𝒙 − −𝒔𝒊𝒏𝒙

𝒅
3. 𝒕𝒂𝒏𝒙 = 𝐬𝐞𝐜 𝟐 𝒙
𝒅𝒙

𝒅
4. 𝒅𝒙
𝒔𝒆𝒄 = 𝒔𝒆𝒄𝒙 𝒕𝒂𝒏𝒙

𝒅
5. 𝒅𝒙
𝒄𝒔𝒄𝒙 = −𝒄𝒔𝒄𝒙 𝒄𝒐𝒕𝒙

𝒅
6. 𝒄𝒐𝒕𝒙 = −𝒄𝐬𝐜 𝟐 𝒙
𝒅𝒙
Derivative of Trigonometric Functions
𝒅
1. 𝒅𝒙
𝒔𝒊𝒏𝒙 = 𝒄𝒐𝒔𝒙

𝒅
2. 𝒅𝒙
𝒄𝒐𝒔𝒙 − −𝒔𝒊𝒏𝒙

𝒅
3. 𝒕𝒂𝒏𝒙 = 𝐬𝐞𝐜 𝟐 𝒙
𝒅𝒙

𝒅
4. 𝒅𝒙
𝒔𝒆𝒄 = 𝒔𝒆𝒄𝒙 𝒕𝒂𝒏𝒙

𝒅
5. 𝒅𝒙
𝒄𝒔𝒄𝒙 = −𝒄𝒔𝒄𝒙 𝒄𝒐𝒕𝒙

𝒅
6. 𝒄𝒐𝒕𝒙 = −𝒄𝐬𝐜 𝟐 𝒙
𝒅𝒙
Derivative of Trigonometric Functions
𝒅
1. 𝒅𝒙
𝒔𝒊𝒏𝒙 = 𝒄𝒐𝒔𝒙

𝒅
2. 𝒅𝒙
𝒄𝒐𝒔𝒙 − −𝒔𝒊𝒏𝒙

𝒅
3. 𝒕𝒂𝒏𝒙 = 𝐬𝐞𝐜 𝟐 𝒙
𝒅𝒙

𝒅
4. 𝒅𝒙
𝒔𝒆𝒄 = 𝒔𝒆𝒄𝒙 𝒕𝒂𝒏𝒙

𝒅
5. 𝒅𝒙
𝒄𝒔𝒄𝒙 = −𝒄𝒔𝒄𝒙 𝒄𝒐𝒕𝒙

𝒅
6. 𝒄𝒐𝒕𝒙 = −𝒄𝐬𝐜 𝟐 𝒙
𝒅𝒙
Derivative of Trigonometric Functions
𝒅
1. 𝒅𝒙
𝒔𝒊𝒏𝒙 = 𝒄𝒐𝒔𝒙

𝒅
2. 𝒅𝒙
𝒄𝒐𝒔𝒙 − −𝒔𝒊𝒏𝒙

𝒅
3. 𝒕𝒂𝒏𝒙 = 𝐬𝐞𝐜 𝟐 𝒙
𝒅𝒙

𝒅
4. 𝒅𝒙
𝒔𝒆𝒄 = 𝒔𝒆𝒄𝒙 𝒕𝒂𝒏𝒙

𝒅
5. 𝒅𝒙
𝒄𝒔𝒄𝒙 = −𝒄𝒔𝒄𝒙 𝒄𝒐𝒕𝒙

𝒅
6. 𝒄𝒐𝒕𝒙 = −𝒄𝐬𝐜 𝟐 𝒙
𝒅𝒙
Derivative of Trigonometric Functions
𝒅
1. 𝒅𝒙
𝒔𝒊𝒏𝒙 = 𝒄𝒐𝒔𝒙

𝒅
2. 𝒅𝒙
𝒄𝒐𝒔𝒙 − −𝒔𝒊𝒏𝒙

𝒅
3. 𝒕𝒂𝒏𝒙 = 𝐬𝐞𝐜 𝟐 𝒙
𝒅𝒙

𝒅
4. 𝒅𝒙
𝒔𝒆𝒄 = 𝒔𝒆𝒄𝒙 𝒕𝒂𝒏𝒙

𝒅
5. 𝒅𝒙
𝒄𝒔𝒄𝒙 = −𝒄𝒔𝒄𝒙 𝒄𝒐𝒕𝒙

𝒅
6. 𝒄𝒐𝒕𝒙 = −𝒄𝐬𝐜 𝟐 𝒙
𝒅𝒙

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