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 to#x# 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#
Since#y=x^(21/2x)# :
#dy/dx=21/2x^(21/2x)(ln(x)+1)#
