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Identical expressions
y=mx^ two +nx+p
y equally mx squared plus nx plus p
y equally mx to the power of two plus nx plus p
y=mx2+nx+p
y=mx²+nx+p
y=mx to the power of 2+nx+p
Similar expressions
y=mx^2-nx+p
y=mx^2+nx-p

The derivative of the function/ y=mx^2+nx+p

Derivative of y=mx^2+nx+p

The solution

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   2          
m*x  + n*x + p

$$m x^{2} + n x + p$$

d /   2          \
--\m*x  + n*x + p/
dx

$$\frac{\partial}{\partial x} \left(m x^{2} + n x + p\right)$$

Transform

Detail solution

Differentiate $m x^{2} + n x + p$ 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: $2 m x$
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: $n$
3. The derivative of the constant $p$ is zero.
The result is: $2 m x + n$

The answer is:

$2 m x + n$

The first derivative [src]

n + 2*m*x

$$2 m x + n$$

Simplify

The second derivative [src]

2*m

$$2 m$$

Simplify

The third derivative [src]

$$0$$

Simplify