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Power Rule

\frac{d}{d x} (x^{n}) = n x^{n - 1}

Differentiate any power of x

derivative of x^5

Chain Rule

\frac{d}{d x} [f (g (x))] = f^{'} (g (x)) \cdot g^{'} (x)

Composite function differentiation

derivative of sin(x^2)

Product Rule

(f g)^{'} = f^{'} g + f g^{'}

Differentiate a product

derivative of x^2 * sin(x)

Quotient Rule

(\frac{f}{g})^{'} = \frac{f ^{'} g - f g ^{'}}{g ^{2}}

Differentiate a quotient

derivative of sin(x)/x

d/dx sin(x)

\frac{d}{d x} sin (x) = cos (x)

Sine derivative

derivative of sin(3x)

d/dx cos(x)

\frac{d}{d x} cos (x) = - sin (x)

Cosine derivative

derivative of cos(x^2)

d/dx eˣ

\frac{d}{d x} e^{x} = e^{x}

Exponential derivative

derivative of e^(2x)

d/dx ln(x)

\frac{d}{d x} ln (x) = \frac{1}{x}

Natural log derivative

derivative of ln(x^2 + 1)

d/dx arctan(x)

\frac{d}{d x} arctan (x) = \frac{1}{1 + x ^{2}}

Arctan derivative

derivative of atan(x)

d/dx xⁿ (General)

\frac{d}{d x} (a x^{n}) = an x^{n - 1}

Polynomial differentiation

derivative of 3x^4 - 2x^2 + 7

50 formulas across 5 categories

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\frac{d}{d x} f (x)

\int_{a}^{b} f (x) d x

\int f (x) d x

lim_{x \to a} f (x)

\sum_{n = 0}^{\infty} \frac{f ^{(n)} ( a )}{n !} (x - a)^{n}

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