Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 3sqrtx
Derivative of tan(x)*cot(x)
Derivative of ax^2+bx+c
Derivative of x^2-49
Canonical form:
ax^2+bx+c
Identical expressions
ax^ two +bx+c
ax squared plus bx plus c
ax to the power of two plus bx plus c
ax2+bx+c
ax²+bx+c
ax to the power of 2+bx+c
Similar expressions
ax^2+bx-c
ax^2-bx+c

The derivative of the function/ ax^2+bx+c

Derivative of ax^2+bx+c

The solution

You have entered [src]

   2          
a*x  + b*x + c

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

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

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

Transform

Detail solution

Differentiate $a x^{2} + b x + c$ 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: $2 a x$
2. 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: $b$
3. The derivative of the constant $c$ is zero.
The result is: $2 a x + b$

The answer is:

$2 a x + b$

The first derivative [src]

b + 2*a*x

$$2 a x + b$$

Simplify

The second derivative [src]

2*a

$$2 a$$

Simplify

The third derivative [src]

$$0$$

Simplify