Mister Exam

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The derivative of the function/ 4x^2-5x

Derivative of 4x^2-5x

The solution

You have entered [src]

   2      
4*x  - 5*x

$$4 x^{2} - 5 x$$

d /   2      \
--\4*x  - 5*x/
dx

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

Transform

Detail solution

Differentiate $4 x^{2} - 5 x$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $8 x$
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: $5$
  So, the result is: $-5$
The result is: $8 x - 5$

The answer is:

$8 x - 5$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-5 + 8*x

$$8 x - 5$$

Simplify

The second derivative [src]

$$8$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of 4x^2-5x