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Derivative of:
Derivative of y=(x^5-2x)^2
Derivative of y=tg^2x-ctg^2x
Derivative of f(x)=-3sin(5x-6)+12x²
Derivative of cos7x
Identical expressions
y=(x^ five - two x)^2
y equally (x to the power of 5 minus 2x) squared
y equally (x to the power of five minus two x) squared
y=(x5-2x)2
y=x5-2x2
y=(x⁵-2x)²
y=(x to the power of 5-2x) to the power of 2
y=x^5-2x^2
Similar expressions
y=(x^5-2x^2)^3*(4x^3-5)^4
y=(x^5-2x^2-1)/x
y=(x^5+2x)^2
sqrt(5x^5-2x^2-4x^3+7)^1/7
y=((x^5-2x^2-1))/x

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

Derivative of y=(x^5-2x)^2

The solution

You have entered [src]

          2
/ 5      \ 
\x  - 2*x/

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

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

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

Transform

Detail solution

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

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

$10 x^{9} - 24 x^{5} + 8 x$

The answer is:

$10 x^{9} - 24 x^{5} + 8 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

/         4\ / 5      \
\-4 + 10*x /*\x  - 2*x/

$$\left(10 x^{4} - 4\right) \left(x^{5} - 2 x\right)$$

Simplify

The second derivative [src]

  /           2                  \
  |/        4\        4 /      4\|
2*\\-2 + 5*x /  + 20*x *\-2 + x //

$$2 \cdot \left(20 x^{4} \left(x^{4} - 2\right) + \left(5 x^{4} - 2\right)^{2}\right)$$

Simplify

The third derivative [src]

     3 /        4\
120*x *\-4 + 6*x /

$$120 x^{3} \cdot \left(6 x^{4} - 4\right)$$

Simplify

The graph

Derivative of y=(x^5-2x)^2