List the various rules that allow us to differentiate constant functions, power functions, polynomials, exponential functions, rational functions, and certain combinations of them, simply and directly, without having to take limits each time?

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List the various rules that allow us to differentiate constant functions,    power functions, polynomials, exponential functions, rational functions, and certain combinations of them,    simply and directly, without having to take limits each time?

Isma Jimenez · Accepted Answer

Step 1 To explain:  The differentiation rule:  Explanation:  The constant rule is used to differentiate constant function:  The differentiation of constant function is 0.  ddx(k)=0  The differentiation of power function rule.  ddx(kxn)=kddx(xn)  Step 2 Power rule of differentiation:  Power rule of differentiation is used to differentiate polynomial function:  ddx(xn)=n∙xn−1  Exponential rule of differentiation:  ddx(ex)=ex  Quotient rule of differentiation:  Quotient rule of differentiation used to differentiate rational function:  ddx(uv)=v⋅u′−v⋅uv2  Chain rule of differentiation:  Chain rule of differentiation used for composite function.  (f(g(x)))′=f′(g(x))g′(x) Thus, the every function has a rule for the differentiation.

List the various rules that allow us to differentiate constant

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