IndietroCalculus Derivatives Formulas
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1/22IndietroSkip to main contentIndietroDerivative of a constant function
The derivative of a constant \(c\) is \(0\). Derivative of a sum
The derivative of \(f(x) + g(x)\) is \(f'(x) + g'(x)\). Product rule
The derivative of \(f(x)g(x)\) is \(f'(x)g(x) + f(x)g'(x)\). Power rule
The derivative of \(x^n\) is \(nx^{n-1}\) for any real number \(n\). Constant multiple rule
The derivative of \(cf(x)\) is \(cf'(x)\) where \(c\) is a constant. Derivative of a difference
The derivative of \(f(x) - g(x)\) is \(f'(x) - g'(x)\). Quotient rule
The derivative of \(\frac{f(x)}{g(x)}\) is \(\frac{g(x)f'(x) - f(x)g'(x)}{(g(x))^2}\). Chain rule
The derivative of \(f(g(x))\) is \(f'(g(x)) \cdot g'(x)\). Derivative of sin x
The derivative of \(\sin x\) is \(\cos x\). Derivative of cos x
The derivative of \(\cos x\) is \(-\sin x\). Derivative of tan x
The derivative of \(\tan x\) is \(\sec^2 x\). Derivative of cot x
The derivative of \(\cot x\) is \(-\csc^2 x\). Derivative of sec x
The derivative of \(\sec x\) is \(\sec x \tan x\). Derivative of csc x
The derivative of \(\csc x\) is \(-\csc x \cot x\). Derivative of sin⁻¹ x
The derivative of \(\sin^{-1} x\) is \(\frac{1}{\sqrt{1 - x^2}}\). Derivative of cos⁻¹ x
The derivative of \(\cos^{-1} x\) is \(-\frac{1}{\sqrt{1 - x^2}}\). Derivative of tan⁻¹ x
The derivative of \(\tan^{-1} x\) is \(\frac{1}{1 + x^2}\). Derivative of sec⁻¹ x
The derivative of \(\sec^{-1} x\) is \(\frac{1}{|x| \sqrt{x^2 - 1}}\). Derivative of e^x
The derivative of \(e^x\) is \(e^x\). Derivative of ln |x|
The derivative of \(\ln |x|\) is \(\frac{1}{x}\). Derivative of b^x
The derivative of \(b^x\) is \(b^x \ln b\). Derivative of log_b x
The derivative of \(\log_b x\) is \(\frac{1}{x \ln b}\).
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