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Differentiation Formulas:

Differentiation of some standard functions
Introduction_to_Quantum_Mechanics
Introduction_to_Quantum_Mechanics
Introduction_to_Quantum_Mechanics
Derivative of (a^x) with respect to x www.faastop.comاللهπ——𝑑𝑑x 𝑎x = 𝑎x𝑙𝑜𝑔ₑ𝑎
Derivative of \(e^x\) with respect to \(x\) www.faastop.comاللهπ——𝑑𝑑x 𝑒x = 𝑒x
Differentiation of Trigonometric Functions
Derivative of \( \sin(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑖𝑛x = 𝑐𝑜𝑠x
Derivative of \( \cos(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠x = -𝑠𝑖𝑛x
Derivative of \( \tan(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑡𝑎𝑛x = 𝑠𝑒𝑐²x
Derivative of \( \cot(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑡x = -𝑐𝑜𝑠𝑒𝑐²x
Derivative of \( \sec(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑒𝑐x = 𝑠𝑒𝑐x 𝑡𝑎𝑛x
Derivative of \( \csc(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠𝑒𝑐x = -𝑐𝑜𝑠𝑒𝑐x 𝑐𝑜𝑡x
Differentiation of Inverse Trigonometric Functions
Derivative of \( \sin^{-1}(x) \) with respect to \( x \) ——𝑑𝑑x 𝑠𝑖𝑛 -1x = ——11-x²www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑖𝑛 -1x = ——11-x²——𝑑𝑑x 𝑠𝑖𝑛 -1x = ——11-x²
Derivative of \( \cos^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠 -1x = ——-11-x²
Derivative of \( \tan^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑡𝑎𝑛 -1x = ——11+x²
Derivative of \( \cot^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑡 -1x = ——-11+x²
Derivative of \( \sec^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑒𝑐 -1x =1|x|x²-1
Derivative of \( \csc^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠𝑒𝑐 -1x =-1|x|x²-1
Differentiation of Hyperbolic Functions
Derivative of \( \sinh(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑖𝑛𝒉x = 𝑐𝑜𝑠𝒉x
Derivative of \( \cosh(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠𝒉x = 𝑠𝑖𝑛𝒉x
Derivative of \( \tanh(x) \) with respect to \( x \)www.faastop.comاللهπ——𝑑𝑑x 𝑡𝑎𝑛𝒉x = 𝑠𝑒𝑐𝒉²x
Derivative of \( \coth(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑡𝒉x = -𝑐𝑜𝑠𝑒𝑐𝒉²x
Derivative of \( \text{sech}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑒𝑐𝒉x = -𝑠𝑒𝑐𝒉x 𝑡𝑎𝑛𝒉x
Derivative of \( \text{csch}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠𝑒𝑐𝒉x = -𝑐𝑜𝑠𝑒𝑐𝒉x 𝑐𝑜𝑡𝒉x
Differentiation of Inverse Hyperbolic Functions
Derivative of \( \sinh^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑖𝑛𝒉 -1x = ——11+x²
Derivative of \( \cosh^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠𝒉 -1x = ——1x²-1
Derivative of \( \tanh^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑡𝑎𝑛𝒉 -1x = ——11 - x²
Derivative of \( \coth^{-1}(x) \) with respect to \( x \) www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑡𝒉 -1x = ——11 - x²
www.faastop.comاللهπ——𝑑𝑑x 𝑠𝑒𝑐𝒉 -1x =-1|x|1-x²
www.faastop.comاللهπ——𝑑𝑑x 𝑐𝑜𝑠𝑒𝑐𝒉 -1x =-1|x|1+x²

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