Calculus 1 - Derivatives Formula Sheet PDF
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Ateneo de Manila University
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This document provides a comprehensive formula sheet for calculus 1, including various derivative rules for different functions such as trigonometric, exponential, logarithmic, and inverse trigonometric functions. It includes the chain rule, product rule, quotient rule, and other essential concepts. It is helpful for students and professionals in mathematics.
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Calculus 1 β Derivatives Formula Sheet: Basic Derivatives: π π π [π] = 0 [π] = 1 [ππ] = π ππ₯ ππ₯ ππ₯...
Calculus 1 β Derivatives Formula Sheet: Basic Derivatives: π π π [π] = 0 [π] = 1 [ππ] = π ππ₯ ππ₯ ππ₯ π [π β π(π)] = π β πβ²(π₯) ππ₯ Trigonometric Derivatives: π π [π¬π’π§ π] = cos π₯ [ππ¨π¬ π] = β sin π₯ ππ₯ ππ₯ π π [πππ§ π] = π ππ 2 π₯ [ππ¨π π] = βππ π 2 π₯ ππ₯ ππ₯ π π [π¬ππ π] = sec π₯ tan π₯ [ππ¬π π] = β csc π₯ cot π₯ ππ₯ ππ₯ The Power Rule: π π [π ] = ππ₯ πβ1 ππ₯ The Product Rule: π [ππ] = π’β² π£ + π’π£β² ππ₯ π [πππ] = π’β² π£π€ + π’π£ β² π€ + π’π£π€β² ππ₯ The Quotient Rule: π π π£π’β² β π’π£β² [ ]= ππ₯ π π£2 The Reciprocal Rule: π π βπ’β² [ ]= 2 ππ₯ π π’ www.Video-Tutor.net The Chain Rule: π π ππ¦ ππ’ = β π π ππ’ ππ₯ π [π(π(π))] = π β² (π(π₯)) β πβ²(π₯) ππ₯ π [π(π(π))] = π β² (π(π’)) β πβ² (π’) β π’β² ππ₯ π [π(π)]π = π[π(π₯)]πβ1 β πβ²(π₯) ππ₯ Trig Derivatives: π π π¬π’π§(π) = cos(π’) π’β² ππ¨π¬(π) = β sin(π’) π’β² βWith Chain Ruleβ ππ₯ ππ₯ π π πππ§(π) = π ππ 2 (π’) π’β² ππ¨π(π) = βππ π 2 (π’) π’β² ππ₯ ππ₯ π π π¬ππ(π) = sec(π’) tan(π’) π’β² ππ¬π(π) = β csc(π’) cot(π’) π’β² ππ₯ ππ₯ Inverse Trig Derivatives: π π’β² π βπ’β² [πππβπ (π)] = [πππβπ (π)] = βWith Chain Ruleβ ππ₯ β1 β π’2 ππ₯ β1 β π’2 π π’β² π βπ’β² [πππβπ (π)] = [πππβπ (π)] = ππ₯ 1 + π’2 ππ₯ 1 + π’2 π π’β² π βπ’β² [πππβπ (π)] = [πππβπ (π)] = ππ₯ |π’|βπ’2 β 1 ππ₯ |π’|βπ’2 β 1 Exponential Derivatives: π π [π ] = π π’ β π’β² ππ₯ π π [π ] = ππ’ β π’β² β ln π ππ₯ Derivatives of Logs: π π’β² [π₯π§ π] = ππ₯ π’ π π’β² [ππππ (π)] = ππ₯ π’ ln π www.Video-Tutor.net Logarithmic Differentiation: π π π£π’β² [π ] = π’π£ [ + π£ β² ln (π’)] ππ₯ π’ Inverse Functions: π βπ 1 [π (π)] = π(π) = π πβπ (π) = π ππ₯ πβ²(π) π βπ 1 [π (π)] = β² β1 ππ₯ π [π (π₯)] Limit Definition: π(π₯ + β) β π(π₯) πβ² (π) = lim ββ0 β Alternative Definition: π(π₯) β π(π) πβ² (π) = lim π₯βπ π₯βπ www.Video-Tutor.net
