Difference between revisions of "Calculus:Derivative of Polynomial Functions"
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#The Product Rule <math>{d (f g) \over d x}'= f {d g \over d x} + g {d f \over d x}</math> | #The Product Rule <math>{d (f g) \over d x}'= f {d g \over d x} + g {d f \over d x}</math> | ||
#The Quotient Rule <math>{d ({f \over g}) \over d x} = { g {d f \over d x} - f {d g \over d x} \over g^2} </math> | #The Quotient Rule <math>{d ({f \over g}) \over d x} = { g {d f \over d x} - f {d g \over d x} \over g^2} </math> | ||
<noinclude> | |||
==Examples== | |||
==Example 1== | |||
Ex1:f(x^4+2x^2+4x+2) | |||
==Example 2== | |||
==Example 3== | |||
==Example 4== | |||
</noinclude> | |||
Revision as of 00:50, 11 August 2021
Derivative of Polynomial Functions
=Newton Derivative of Polynomial Functions=
- The sum rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (f+g)'=f'+g'}
- The Difference Rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (f-g)'=f'-g'}
- The Product Rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (f*g)'=f*g'+ g*f'}
- The Quotient Rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ({f \over g})' = {(gf'-fg') \over g^2} }
=Leibniz Derivative of Polynomial Functions=
- The sum rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {d (f+g) \over d x} ={d f \over d x} + {d g \over d x}}
- The Difference Rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {d (f-g) \over d x}={d f \over d x} - {d g \over d x}}
- The Product Rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {d (f g) \over d x}'= f {d g \over d x} + g {d f \over d x}}
- The Quotient Rule Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {d ({f \over g}) \over d x} = { g {d f \over d x} - f {d g \over d x} \over g^2} }
Examples
Example 1
Ex1:f(x^4+2x^2+4x+2)