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Derivative of:
Derivative of 6^(x^2-8x+28)
Derivative of x/16
Derivative of sin9x
Derivative of ln(x^2-2)
Identical expressions
y+(t+ two)y^ two
y plus (t plus 2)y squared
y plus (t plus two)y to the power of two
y+(t+2)y2
y+t+2y2
y+(t+2)y²
y+(t+2)y to the power of 2
y+t+2y^2
Similar expressions
y+(t-2)y^2
y-(t+2)y^2

The derivative of the function/ y+(t+2)y^2

Derivative of y+(t+2)y^2

The solution

You have entered [src]

             2
y + (t + 2)*y

$$y^{2} \left(t + 2\right) + y$$

y + (t + 2)*y^2

Detail solution

Differentiate $y^{2} \left(t + 2\right) + y$ term by term:
1. Apply the power rule: $y$ goes to $1$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $y^{2}$ goes to $2 y$
  So, the result is: $2 y \left(t + 2\right)$
The result is: $2 y \left(t + 2\right) + 1$
Now simplify:

$2 y \left(t + 2\right) + 1$

The answer is:

$2 y \left(t + 2\right) + 1$

The first derivative [src]

1 + 2*y*(t + 2)

$$2 y \left(t + 2\right) + 1$$

Simplify

The second derivative [src]

2*(2 + t)

$$2 \left(t + 2\right)$$

Simplify

The third derivative [src]

$$0$$

Simplify