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Question Number 75402 by vishalbhardwaj last updated on 10/Dec/19

$$\mathrm{Explain}\mathrm{the}\mathrm{proof}$$$$\mathrm{with}\mathrm{appropriate}$$$$\mathrm{diagram}:$$$${\mathrm{Lim}}_{h\to 0}\frac{f\left(x\right)-f(x-h)}{-h}$$$$=\frac{dy}{dx},\mathrm{where}y=f\left(x\right)$$

Commented by Kunal12588 last updated on 10/Dec/19

$${isn}^{\prime }titthedefinationofderivative?$$$$firstprinciple$$$$\frac{dy}{dx}=\underset{\mathrm{\Delta }x\to 0}{lim}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\underset{\mathrm{\Delta }x\to 0}{lim}\frac{f(x+\mathrm{\Delta }x)-f\left(x\right)}{\mathrm{\Delta }x}$$

Commented by vishalbhardwaj last updated on 10/Dec/19

$$\mathrm{sir}\mathrm{this}\mathrm{is}\mathrm{LHD}$$

Commented by Kunal12588 last updated on 10/Dec/19

$$\mathrm{\Delta }x=0-h$$$$\Rightarrow \mathrm{\Delta }x=-h$$$$\mathrm{\Delta }x\to 0\Rightarrow h\to 0$$$$LHD=\underset{h\to 0}{lim}\frac{f(x-h)-f\left(x\right)}{-h}$$

Commented by vishalbhardwaj last updated on 12/Dec/19

$$\mathrm{please}\mathrm{explain}\mathrm{the}\mathrm{proof}\mathrm{of}\mathrm{this}$$$$\mathrm{with}\mathrm{the}\mathrm{help}\mathrm{of}\mathrm{diagram}$$

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