Question #c9528

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Answer 1 · 2017-12-21T03:10:07

#d/dx(1/(2sqrtx))=1/(4sqrt(x^3))#

The derivative of #1/(2sqrtx)# can be rewritten as:

#1/2d/dx(1/sqrtx)#

Thus, #d/dx(1/sqrtx)->x^(-1/2)#

By the power rule: #d/dx(x^a)=a*x^(a-1)#

#1/sqrtx->x^(-1/2)->-1/2x^(-1/2-1)=-1/2x^(-3/2)#

Simplifying...

#1/2d/dx(1/sqrtx)=1/2(-1/(2x^(3/2)))=-1/(4x^(3/2))=1/(4sqrt(x^3))#