• Math Doubts
• Differential calculus
• Differentiation
• Rules
• Properties

The functions, which involve in basic mathematical operations are appeared in differential calculus. The derivatives of such functions require some special properties to find the differentiation. The following four properties are useful to find the derivatives of the functions, which involve in fundamental operations. So, let’s learn the following differentiation properties with proofs and example problems.

Sum Rule

$\dfrac{d}{dx}{\Big(f{(x)}+g{(x)}\Big)}$ $\,=\,$ $\dfrac{d}{dx}{f{(x)}}$ $+$ $\dfrac{d}{dx}{g{(x)}}$

Difference Rule

$\dfrac{d}{dx}{\Big(f{(x)}-g{(x)}\Big)}$ $\,=\,$ $\dfrac{d}{dx}{f{(x)}}$ $-$ $\dfrac{d}{dx}{g{(x)}}$

Product Rule

$\dfrac{d}{dx}{\Big(f(x) \times g(x)\Big)}$ $\,=\,$ $f(x)\dfrac{d}{dx}{g(x)}$ $+$ $g(x)\dfrac{d}{dx}{f(x)}$

Quotient Rule

$\dfrac{d}{dx}{\Bigg(\dfrac{f(x)}{g(x)}\Bigg)}$ $\,=\,$ $\dfrac{g(x)\dfrac{d}{dx}{f(x)}-f(x)\dfrac{d}{dx}{g(x)}}{g{(x)}^2}$

Ashok Kumar, B.E.

Founder of Math Doubts

A Specialist in Mathematics, Physics, and Engineering with 14 years of experience helping students master complex concepts from basics to advanced levels with clarity and precision.

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