Question

How to find the derivative 5x²-2x+1

Answer 1

U can with practical method or with definition.


`f(x)=5x^2-2x+1\\ \\f'(x)=2*5x^(2-1)-1*2x^(1-1)+0\\ \\f'(x)=10x-2\\ \\f'(x)=2(5x-1)`

Answer 2

What you need to know:


`y=k{ x }^( n )\\ \\ \ln { y } =\ln { \left( k{ x }^( n ) \right) }`


`\\ \\ \ln { y } =\ln { k } +\ln { \left( { x }^( n ) \right) } \\ \\ \ln { y } =\ln { k } +n\ln { x }`


`\\ \\ \frac { 1 }{ y } \cdot \frac { dy }{ dx } =\frac { n }{ x } \\ \\ y\cdot \frac { 1 }{ y } \cdot \frac { dy }{ dx } =\frac { n }{ x } \cdot y`


`\\ \\ \frac { dy }{ dx } =n{ x }^( -1 )\cdot k{ x }^( n )\\ \\ \frac { dy }{ dx } =kn{ x }^( -1+n )`


`\\ \\ \frac { dy }{ dx } =kn{ x }^( n-1 )`

If this is the case, when:


`y=5{ x }^( 2 )-2x+1`

dy/dx is...


`\\ \\ \frac { dy }{ dx } =5\cdot 2{ x }^( 2-1 )-2\cdot 1{ x }^( 1-1 )\\ \\ \frac { dy }{ dx } =10x-2\cdot { x }^( 0 )`


`\\ \\ \frac { dy }{ dx } =10x-2`