How do you find the derivative of #x+sqrt(x)#?

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Answer 1 · 2018-03-21T22:35:59

#color(blue)(1+1/2x^(-1/2))# or #color(blue)(1+1/(2sqrt(x)))#

#f(x)=x+sqrt(x)#

Rewriting as:

#f(x)=x+x^(1/2)#

We can differentiate this using the power rule:

The Power Rules states that:

#dy/dx(ax^n)=nax^(n-1)#

#dy/dx# is distributive over the sum, so:

#dy/dx(ax^2+bx+c)=dy/dx(ax^2)+dy/dx(bx)+dy/dx(c)#

Differentiating #f(x)#

#dy/dx(x+x^(1/2))=1*x^(1-1)+1/2*x^(1/2-1)#

#=x^0+1/2x^(-1/2)=color(blue)(1+1/2x^(-1/2))# or #color(blue)(1+1/(2sqrt(x)))#