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Derivative of:
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Identical expressions
y=x^ three (x^ two – five)
y equally x cubed (x squared –5)
y equally x to the power of three (x to the power of two – five)
y=x3(x2–5)
y=x3x2–5
y=x³(x²–5)
y=x to the power of 3(x to the power of 2–5)
y=x^3x^2–5

The derivative of the function/ y=x^3(x^2–5)

Derivative of y=x^3(x^2–5)

The solution

You have entered [src]

 3 / 2    \
x *\x  - 5/

$$x^{3} \left(x^{2} - 5\right)$$

d / 3 / 2    \\
--\x *\x  - 5//
dx

$$\frac{d}{d x} x^{3} \left(x^{2} - 5\right)$$

Transform

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x^{3}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
$g{\left(x \right)} = x^{2} - 5$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{2} - 5$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $\left(-1\right) 5$ is zero.
  The result is: $2 x$
The result is: $2 x^{4} + 3 x^{2} \left(x^{2} - 5\right)$
Now simplify:

$5 x^{2} \left(x^{2} - 3\right)$

The answer is:

$5 x^{2} \left(x^{2} - 3\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   4      2 / 2    \
2*x  + 3*x *\x  - 5/

$$2 x^{4} + 3 x^{2} \left(x^{2} - 5\right)$$

Simplify

The second derivative [src]

    /          2\
2*x*\-15 + 10*x /

$$2 x \left(10 x^{2} - 15\right)$$

Simplify

The third derivative [src]

   /        2\
30*\-1 + 2*x /

$$30 \cdot \left(2 x^{2} - 1\right)$$

Simplify

The graph

Derivative of y=x^3(x^2–5)