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Derivative of:
Derivative of x*log(x)
Derivative of x^4-2x^2+1
Derivative of (x^2-3x)^5
Derivative of log10(3x+1)
Identical expressions
(x^ two -3x)^ five
(x squared minus 3x) to the power of 5
(x to the power of two minus 3x) to the power of five
(x2-3x)5
x2-3x5
(x²-3x)⁵
(x to the power of 2-3x) to the power of 5
x^2-3x^5
Similar expressions
(x^2+3x)^5
(3x^2-3x)^5

The derivative of the function/ (x^2-3x)^5

Derivative of (x^2-3x)^5

The solution

You have entered [src]

          5
/ 2      \ 
\x  - 3*x/

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

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

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

Transform

Detail solution

Let $u = x^{2} - 3 x$ .
Apply the power rule: $u^{5}$ goes to $5 u^{4}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 3 x\right)$ :
1. Differentiate $x^{2} - 3 x$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $3$
    So, the result is: $-3$
  The result is: $2 x - 3$
The result of the chain rule is:

$5 \cdot \left(2 x - 3\right) \left(x^{2} - 3 x\right)^{4}$
Now simplify:

$x^{4} \left(x - 3\right)^{4} \cdot \left(10 x - 15\right)$

The answer is:

x^{4} \left(x - 3\right)^{4} \cdot \left(10 x - 15\right)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          4             
/ 2      \              
\x  - 3*x/ *(-15 + 10*x)

\left(10 x - 15\right) \left(x^{2} - 3 x\right)^{4}

Simplify

The second derivative [src]

    3         3 /            2             \
10*x *(-3 + x) *\2*(-3 + 2*x)  + x*(-3 + x)/

10 x^{3} \left(x - 3\right)^{3} \left(x \left(x - 3\right) + 2 \left(2 x - 3\right)^{2}\right)

Simplify

The third derivative [src]

    2         2            /          2               \
60*x *(-3 + x) *(-3 + 2*x)*\(-3 + 2*x)  + 2*x*(-3 + x)/

60 x^{2} \left(x - 3\right)^{2} \cdot \left(2 x - 3\right) \left(2 x \left(x - 3\right) + \left(2 x - 3\right)^{2}\right)

Simplify

The graph

Derivative of (x^2-3x)^5