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Derivative of:
Derivative of x^x^x
Derivative of x^-6
Derivative of x^-11
Derivative of (x+5)/(x+1)
Identical expressions
y=x^ two (x- eight)+ ten
y equally x squared (x minus 8) plus 10
y equally x to the power of two (x minus eight) plus ten
y=x2(x-8)+10
y=x2x-8+10
y=x²(x-8)+10
y=x to the power of 2(x-8)+10
y=x^2x-8+10
Similar expressions
y=x^2(x-8)-10
y=x^2(x+8)+10

The derivative of the function/ y=x^2(x-8)+10

Derivative of y=x^2(x-8)+10

The solution

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 2             
x *(x - 8) + 10

$$x^{2} \left(x - 8\right) + 10$$

d / 2             \
--\x *(x - 8) + 10/
dx

$$\frac{d}{d x} \left(x^{2} \left(x - 8\right) + 10\right)$$

Transform

Detail solution

Differentiate $x^{2} \left(x - 8\right) + 10$ term by term:
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  $g{\left(x \right)} = x - 8$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Differentiate $x - 8$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $\left(-1\right) 8$ is zero.
    The result is: $1$
  The result is: $x^{2} + 2 x \left(x - 8\right)$
2. The derivative of the constant $10$ is zero.
The result is: $x^{2} + 2 x \left(x - 8\right)$
Now simplify:

$x \left(3 x - 16\right)$

The answer is:

$x \left(3 x - 16\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2              
x  + 2*x*(x - 8)

$$x^{2} + 2 x \left(x - 8\right)$$

Simplify

The second derivative [src]

2*(-8 + 3*x)

$$2 \cdot \left(3 x - 8\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of y=x^2(x-8)+10