Derivative Rules

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Derivative Rules We know that if $displaystyle y=f(x)$ then the derivative is defined to be $displaystyle f'(x)=underset{{hto 0}}{mathop{{lim }}},frac{{f(x+h)-f(x)}}{h}$ Some notions we use when we write the derivative are: $ displaystyle y’=f'(x)=frac{{df}}{{dx}}=frac{{dy}}{{dx}}$ Determining the derivative of a function using the definition sometimes it  requires a lot of work and it’s easy to make mistakes so […]

The derivative using the limit definition

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The derivative using the limit definition Definition The derivative of the function $ displaystyle f$ at the point a is the limit when $ displaystyle hto 0$ of the function, if this limit exists. We label it f´(a) and $displaystyle f'(a)=underset{{hto 0}}{mathop{{lim }}},frac{{f(a+h)-f(a)}}{h}$ When the function$ displaystyle f$ is derivative on the point $ displaystyle […]