How do you find the derivative of #y =4/sqrt(x)#?

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Answer 1 · 2014-08-02T00:05:33

When you're differentiating things involving radicals, it's never a bad idea to rewrite the radicals as rational exponents:

#y = 4x^(-1/2)#

Now, this is easily differentiated using the power rule:

#dy/dx = (-1/2)*4x^(-3/2)#

Simplified:

#dy/dx = -2x^(-3/2)#

And, if we want to put the answer in radical form:

#dy/dx = -2/(sqrt(x^3))#