What is the derivative of sqrt7 times x + sqrt2x

I guess you mean the derivative of:

√7x + √2x, if so then:

Remember that the derivative of √u = 1 / (2√u). u'

if 7x = u, then u' = 7, hence the derivative of √7x is 7 / (2√7x)

Use same logic for √2x and you will find:

y' = 7 / (2√7x) + x/√2x