Mister Exam

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The derivative of the function/ ax+bx²

Derivative of ax+bx²

The solution

You have entered [src]

         2
a*x + b*x

$$b x^{2} + a x$$

d /         2\
--\a*x + b*x /
dx

$$\frac{\partial}{\partial x} \left(b x^{2} + a x\right)$$

Transform

Detail solution

Differentiate $a x + b x^{2}$ 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: $x$ goes to $1$
  So, the result is: $a$
2. 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: $2 b x$
The result is: $a + 2 b x$

The answer is:

$a + 2 b x$

The first derivative [src]

a + 2*b*x

$$2 b x + a$$

Simplify

The second derivative [src]

2*b

$$2 b$$

Simplify

The third derivative [src]

$$0$$

Simplify