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(x²-3)⁵
The derivative of the function/ (x²-3)⁵

Derivative of (x²-3)⁵

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

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The solution

You have entered [src] 
        5
/ 2    \ 
\x  - 3/
(x2−3)5\left(x^{2} - 3\right)^{5} 
  /        5\
d |/ 2    \ |
--\\x  - 3/ /
dx
ddx(x2−3)5\frac{d}{d x} \left(x^{2} - 3\right)^{5}
Transform
Detail solution

  1. Let u=x2−3u = x^{2} - 3.

  2. Apply the power rule: u5u^{5} goes to 5u45 u^{4}

  3. Then, apply the chain rule. Multiply by ddx(x2−3)\frac{d}{d x} \left(x^{2} - 3\right):

    1. Differentiate x2−3x^{2} - 3 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant (−1)3\left(-1\right) 3 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    10x(x2−3)410 x \left(x^{2} - 3\right)^{4}

  4. Now simplify:

    10x(x2−3)410 x \left(x^{2} - 3\right)^{4}

The answer is:

10x(x2−3)410 x \left(x^{2} - 3\right)^{4}

The graph
02468-8-6-4-2-1010-2000000000020000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
             4
     / 2    \ 
10*x*\x  - 3/
10x(x2−3)410 x \left(x^{2} - 3\right)^{4}
Simplify
The second derivative [src] 
            3            
   /      2\  /        2\
10*\-3 + x / *\-3 + 9*x /
10(x2−3)3⋅(9x2−3)10 \left(x^{2} - 3\right)^{3} \cdot \left(9 x^{2} - 3\right)
Simplify
The third derivative [src] 
               2            
      /      2\  /        2\
240*x*\-3 + x / *\-3 + 3*x /
240x(x2−3)2⋅(3x2−3)240 x \left(x^{2} - 3\right)^{2} \cdot \left(3 x^{2} - 3\right)
Simplify
The graph
Derivative of (x²-3)⁵
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