The calculator will find the derivative of
ln(x+1), with steps shown.
Related calculators:
Logarithmic Differentiation Calculator,
Implicit Differentiation Calculator with Steps
Solution
The function ln(x+1) is the composition f(g(x)) of two functions f(u)=ln(u) and g(x)=x+1.
Apply the chain rule dxd(f(g(x)))=dud(f(u))dxd(g(x)):
(dxd(ln(x+1)))=(dud(ln(u))dxd(x+1))The derivative of the natural logarithm is dud(ln(u))=u1:
(dud(ln(u)))dxd(x+1)=(u1)dxd(x+1)Return to the old variable:
(u)dxd(x+1)=(x+1)dxd(x+1)The derivative of a sum/difference is the sum/difference of derivatives:
x+1(dxd(x+1))=x+1(dxd(x)+dxd(1))The derivative of a constant is 0:
x+1(dxd(1))+dxd(x)=x+1(0)+dxd(x)Apply the power rule dxd(xn)=nxn−1 with n=1, in other words, dxd(x)=1:
x+1(dxd(x))=x+1(1)Thus, dxd(ln(x+1))=x+11.
Answer
dxd(ln(x+1))=x+11A