GENERAL DERIVATIVE RULES Constant Rule Constant Multiple Rule Sum Rule Difference Rule Product Rule Quotient Rule Chain Rule π [π] = 0 ππ₯ π [ππ(π₯)] = ππ ′ (π₯) ππ₯ π [π(π₯) + π(π₯)] = π ′ (π₯) + π′ (π₯) ππ₯ π [π(π₯) − π(π₯)] = π ′ (π₯) − π′ (π₯) ππ₯ π [π(π₯) β π(π₯)] = π ′ (π₯)π(π₯) + π(π₯)π′ (π₯) ππ₯ π π(π₯) π(π₯)π ′ (π₯) − π(π₯)π′ (π₯) [ ]= [π(π₯)]2 ππ₯ π(π₯) π [π(π(π₯))] = π ′ (π(π₯))π′ (π₯) ππ₯ DERIVATIVE RULES FOR PARTICULAR FUNCTIONS FUNCTION BASIC RULE Power Sine Cosine Tangent Cosecant Secant Cotangent Arcsine Arccosine Arctangent Arccosecant Arcsecant Arccotangent Exponential (base e) Exponential (base a) Natural Logarithm Logarithm (base a) CHAIN RULE π π [π₯ ] = ππ₯ π−1 ππ₯ TRIGONOMETRIC FUNCTIONS π [sin(π₯)] = cos(π₯) ππ₯ π [cos(π₯)] = −sinβ‘(π₯) ππ₯ π [tan(π₯)] = sec 2 (π₯) ππ₯ π [csc(π₯)] = β‘ − csc(π₯) cotβ‘(π₯) ππ₯ π [sec(π₯)] = β‘ sec(π₯) tanβ‘(π₯) ππ₯ π [cot(π₯)] = − csc 2 (π₯) ππ₯ INVERSE TRIGONOMETRIC FUNCTIONS π 1 sin−1 (π₯) = β‘ ππ₯ √1 − π₯ 2 π −1 cos −1 (π₯) = β‘ ππ₯ √1 − π₯ 2 π 1 tan−1 (π₯) = β‘ ππ₯ 1 + π₯2 π −1 csc −1 (π₯) = β‘ ππ₯ |π₯|√π₯ 2 − 1 π [csc(π’)] = β‘ − csc(π’) cotβ‘(π’) β π’′ ππ₯ π [sec(π’)] = β‘ sec(π’) tanβ‘(π’) β‘ β π’′ ππ₯ π [cot(π’)] = − csc 2 (π’) β π’′ ππ₯ π 1 sec −1 (π₯) = β‘ ππ₯ |π₯|√π₯ 2 − 1 π 1 sec −1 (π’) = β‘ β π’′ ππ₯ |π’|√π’2 − 1 π −1 cot −1 (π₯) = β‘ ππ₯ 1 + π₯2 EXPONENTIAL FUNCTIONS π π₯ [π ] = π π₯ ππ₯ π π₯ [π ] = π π₯ ln(π) ππ₯ LOGARITHMIC FUNCTIONS π 1 [ln(π₯)] = ππ₯ π₯ π 1 [log π (π₯)] = ππ₯ π₯ β ln(π) π −1 cot −1 (π’) = β‘ β π’′ ππ₯ 1 + π’2 Created by Sarah Carter | @mathequalslove |mathequalslove.net | π π [π’ ] = ππ’π−1 β π’′ ππ₯ π [sin π’] = cos(π’) β π’′ ππ₯ π [cos π’] = −sin(π’) β π’′ ππ₯ π [tan(π’)] = sec 2 (π’) β π’′ ππ₯ π 1 sin−1 (π’) = β‘ β π’′ ππ₯ √1 − π’2 π −1 cos −1 (π’) = β‘ β π’′ ππ₯ √1 − π’2 π 1 tan−1 (π’) = β‘ β π’′ ππ₯ 1 + π’2 π −1 csc −1 (π’) = β‘ β π’′ ππ₯ |π’|√π’2 − 1 π π’ [π ] = π π’ β π’′ ππ₯ π π’ [π ] = ππ’ ln(π) β π’′ ππ₯ π 1 π’′ [ln(π’)] = β π’′ β‘ππβ‘ ππ₯ π’ π’ π 1 [log π (π’)] = β π’′ ππ₯ π’ β ln(π)