Differentiate

Question

g(x)=x^(2^1/2)+(x^3/2^1/2)+e^(2^1/2)+(2e^x)^1/2

Answer 1

Let's rewrite that as
g(x) = x^(5/2) + x^(3/4) + sqrt2*e^(x/2) + e^5/2

Differentiate the terms one at a time and add the results. Since e^5/2 is a constant, the derivative of that term is zero. Remember the general rule for the derivative of x^n:
d/dx (x^n) = n x^(n-1)

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