The calculator will find the derivative of
eax with respect to
x, with steps shown.
Related calculators:
Logarithmic Differentiation Calculator,
Implicit Differentiation Calculator with Steps
Solution
The function eax is the composition f(g(x)) of two functions f(u)=eu and g(x)=ax.
Apply the chain rule dxd(f(g(x)))=dud(f(u))dxd(g(x)):
(dxd(eax))=(dud(eu)dxd(ax))The derivative of the exponential is dud(eu)=eu:
(dud(eu))dxd(ax)=(eu)dxd(ax)Return to the old variable:
e(u)dxd(ax)=e(ax)dxd(ax)Apply the constant multiple rule dxd(cf(x))=cdxd(f(x)) with c=a and f(x)=x:
eax(dxd(ax))=eax(adxd(x))Apply the power rule dxd(xn)=nxn−1 with n=1, in other words, dxd(x)=1:
aeax(dxd(x))=aeax(1)Thus, dxd(eax)=aeax.
Answer
dxd(eax)=aeaxA