What is the derivative of #y =x^2-5x+10#?

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Answer 1 · 2016-05-26T03:01:37

#d/dx (x^2−5x+10)=2x-5#

The power rule gives the derivative of an expression of the form #x^n# .

#d/dx x^n=n*x^{n-1}#

We will also need the linearity of the derivative

#d/dx (a*f(x)+b*g(x))=a*d/dx(f(x))+b*d/dx (g(x)) #

and that the derivative of a constant is zero.

We have

#f(x)=x^2−5x+10#

#d/dxf(x)=d/dx (x^2−5x+10)=d/dx (x^2)−5d/dx(x)+d/dx(10)#

#=2*x^1-5*1*x^0+0=2x-5#