Question #7e670
1 Answer
Apr 8, 2017
Explanation:
y=sqrt(x)^(21x)
y=x^(21/2x)
ln(y)=ln(x^(21/2x))=21/2xln(x)
Take the derivative with respect tox for both sides:
d/dxln(y)=d/dx(21/2xln(x))
Using the chain rule for the left-hand side and the product rule for the right-hand side:
(dy/dx)/y=21/2(ln(x)+1)
dy/dx=21/2(ln(x)+1)y
Sincey=x^(21/2x) :
dy/dx=21/2x^(21/2x)(ln(x)+1)
