Find the derivative of the function below by simplifying ? F(x) =( x - 7x √x) ÷ √x

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Answer 1 · 2017-03-24T04:28:50

#f'(x)=(1-14sqrtx)/(2sqrtx)#

#f(x)=(x-7xsqrtx)/sqrtx#

Splitting up the fraction gives two distinct terms:

#x/sqrtx=(sqrtxsqrtx)/sqrtx=sqrtx#

#(7xsqrtx)/sqrtx=7x#

So:

#f(x)=sqrtx-7x#

Which can be differentiated using the power rule:

#f(x)=x^(1/2)-7x^1#

#f'(x)=1/2x^(-1/2)-7(1)x^0#

#f'(x)=1/(2sqrtx)-7#

Finding a common denominator:

#f'(x)=(1-14sqrtx)/(2sqrtx)#