Derivative of ex

How to find the derivative of the given function by using the derivative of ex: formula, 2 examples, and their solutions.

Formula

Formula

The derivative of ex, [ex]',
is itself: ex.

Example 1

Example

Solution

x2ex is the product of x2 and ex.

So the derivative of the product is,
the derivative of x2, 2x1
times ex
plus
x2
times, the derivative of ex, ex.

2x1⋅ex + x2⋅ex = ex(x2 + 2x).

Common Monomial Factor

ex(x2 + 2x) is the derivative of x2ex.

Example 2

Example

Solution

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
times,
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.