Derivative of ex
How to find the derivative of the given function by using the derivative of ex: formula, 2 examples, and their solutions.
The derivative of ex, [ex]',
is itself: ex.
2x1⋅ex + x2⋅ex = ex(x2 + 2x).
Common Monomial Factor
ex(x2 + 2x) is the derivative of x2ex.
y = ex2 - 4x is a composite function of
y = e(whole) and (whole) = x2 - 4x.
So the derivative of the composite function is,
the derivative of the outer function ex2 - 4x, ex2 - 4x
the derivative of the inner function x2 - 4x, 2x1 - 4.
ex2 - 4x(2x1 - 4) = (2x - 4)ex2 - 4x
So (2x - 4)ex2 - 4x is the derivative of ex2 - 4x.