If y=xnlogx+x(logx)n, then dydx is equal to
xn−1(1+nlogx)+(logx)n−1(n+logx)
xn−2(1+nlogx)+(logx)n−1(n+logx)
xn−1(1+nlogx)+(logx)n−1(n−logx)
None of these
Finding the value of dydx:
The given differential function is y=xnlogx+x(logx)n.
Differentiate the given equation with respect to x.
dydx=nxn−1logx+xn1x+logxn+xnlogxn−11x[∵dxydx=xdydx+ydxdx,dxndx=nxn-1,dlogxdx=1x]=xn−1nlogx+1+logxn−1logx+n
Hence, the correct option is A.
Complete the Tables
Expression
Term with factor of x
Coefficient of x
3x-5
3x
3
8-x+y
2z-5xz