List the various rules that allow us to differentiate constant

remolatg

remolatg

Answered question

2021-10-07

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?

Answer & Explanation

Isma Jimenez

Isma Jimenez

Skilled2021-10-08Added 84 answers

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)=nxn1
Exponential rule of differentiation:
ddx(ex)=ex
Quotient rule of differentiation:
Quotient rule of differentiation used to differentiate rational function:
ddx(uv)=vuvuv2
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.

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