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Formulas of Differential Calculus | Derivative Rules | ক্যালকুলাস এর সূত্রসমূহ

Formulas of Differential Calculus | Derivative Rules | ক্যালকুলাস এর সূত্রসমূহ


\frac{d}{dx}(c)  = 0                             [where, c is single constant]

\frac{d}{dx}(cu) = c \frac {d}{dx} (u)   [where, c is with a variable]

\frac{d}{dx} (xn) = nxn-1

\frac{d}{dx} (\sqrt {x})= \frac {1}{2\sqrt{x}}

\frac{d}{dx} (ex)= ex

\frac{d}{dx} (emx)= memx

\frac{d}{dx} (e-mx)= -me-mx

\frac{d}{dx} (loga x)= \frac {1}{x} logae

\frac{d}{dx} (log x)= \frac {1}{x}

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

\frac{d}{dx} (sin mx)= m cos mx

\frac{d}{dx} (cos x)= - sin x

\frac{d}{dx} (cos mx)= - m sin mx

\frac{d}{dx} (sec x)= sec x. tan x

\frac{d}{dx} (cosec x)= -cosec x. cot x

\frac{d}{dx} (tan x)= sec2 x

\frac{d}{dx}3 (cot x)= -cosec2 x

\frac{d}{dx} (sin-1) = 1  \over { \sqrt{1-x^2 }}

\frac{d}{dx} (cos-1)= -1  \over { \sqrt{1-x^2 }}

\frac{d}{dx} (tan-1)= \frac{1}{1+x^2}

\frac{d}{dx} (uv)= u \frac {d}{dx} (v) + v \frac {d}{dx} (u)

\frac{d}{dx} (uvw) = vw \frac {d}{dx} (u) + uw \frac {d}{dx} (v) + uv \frac {d}{dx}( w )

\frac {d}{dx} (\frac {u}{v}) = \frac{v\frac{\mathrm{d}}{\mathrm{d} x} ( u )-u\frac{\mathrm{d} }{\mathrm{d} x} ( v )}{v^{2}}


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