Mister Exam

Derivative of y=(x²+3x-5)²

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
              2
/ 2          \ 
\x  + 3*x - 5/ 
$$\left(\left(x^{2} + 3 x\right) - 5\right)^{2}$$
(x^2 + 3*x - 5)^2
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
          / 2          \
(6 + 4*x)*\x  + 3*x - 5/
$$\left(4 x + 6\right) \left(\left(x^{2} + 3 x\right) - 5\right)$$
The second derivative [src]
  /               2              \
2*\-10 + (3 + 2*x)  + 2*x*(3 + x)/
$$2 \left(2 x \left(x + 3\right) + \left(2 x + 3\right)^{2} - 10\right)$$
The third derivative [src]
12*(3 + 2*x)
$$12 \left(2 x + 3\right)$$
The graph
Derivative of y=(x²+3x-5)²