This handwritten derivative formula sheet summarizes the 25 most important derivative rules in calculus. It includes power, product, quotient, chain, exponential, logarithmic, trigonometric, and inverse trigonometric derivatives, making it a useful reference for studying, revision, and exam preparation.
- $\dfrac{d}{dx}(c) = 0$ ($c$ is a constant)
- $\dfrac{d}{dx}(x) = 1$
- $\dfrac{d}{dx}(x^n) = nx^{n-1}$ ($n$ is a real number)
- $\dfrac{d}{dx}(kf(x)) = kf'(x)$ ($k$ is a constant)
- $\dfrac{d}{dx}(f(x) + g(x)) = f'(x) + g'(x)$
- $\dfrac{d}{dx}(f(x) - g(x)) = f'(x) - g'(x)$
- $\dfrac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)$ (Product Rule)
- $\dfrac{d}{dx}\left(\dfrac{f(x)}{g(x)}\right) = \dfrac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$ (Quotient Rule)
- $\dfrac{d}{dx}(f(g(x))) = f'(g(x)) \cdot g'(x)$ (Chain Rule)
- $\dfrac{d}{dx}(e^x) = e^x$
- $\dfrac{d}{dx}(a^x) = a^x \ln a$ ($a > 0,\ a \neq 1$)
- $\dfrac{d}{dx}(\ln x) = \dfrac{1}{x}$ ($x > 0$)
- $\dfrac{d}{dx}(\log_a x) = \dfrac{1}{x \ln a}$ ($a > 0,\ a \neq 1,\ x > 0$)
- $\dfrac{d}{dx}(\sin x) = \cos x$
- $\dfrac{d}{dx}(\cos x) = -\sin x$
- $\dfrac{d}{dx}(\tan x) = \sec^2 x$
- $\dfrac{d}{dx}(\cot x) = -\csc^2 x$
- $\dfrac{d}{dx}(\sec x) = \sec x \tan x$
- $\dfrac{d}{dx}(\csc x) = -\csc x \cot x$
- $\dfrac{d}{dx}(\arcsin x) = \dfrac{1}{\sqrt{1 - x^2}}$ ($|x| < 1$)
- $\dfrac{d}{dx}(\arccos x) = -\dfrac{1}{\sqrt{1 - x^2}}$ ($|x| < 1$)
- $\dfrac{d}{dx}(\arctan x) = \dfrac{1}{1 + x^2}$
- $\dfrac{d}{dx}(\text{arccot}, x) = -\dfrac{1}{1 + x^2}$
- $\dfrac{d}{dx}(|x|) = \begin{cases} 1, & x > 0 \ -1, & x < 0 \end{cases}$ ($x \neq 0$)
- $\dfrac{d}{dx}(\sqrt{x}) = \dfrac{1}{2\sqrt{x}}$ ($x > 0$)
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25 Derivative Formulas Every Student Should Know.pdf
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