Mister Exam

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The derivative of the function/ 3t^2+4t+1

Derivative of 3t^2+4t+1

The solution

You have entered [src]

   2          
3*t  + 4*t + 1

$$3 t^{2} + 4 t + 1$$

d /   2          \
--\3*t  + 4*t + 1/
dt

$$\frac{d}{d t} \left(3 t^{2} + 4 t + 1\right)$$

Transform

Detail solution

Differentiate $3 t^{2} + 4 t + 1$ 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: $t^{2}$ goes to $2 t$
  So, the result is: $6 t$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $t$ goes to $1$
  So, the result is: $4$
3. The derivative of the constant $1$ is zero.
The result is: $6 t + 4$

The answer is:

$6 t + 4$

The first derivative [src]

4 + 6*t

$$6 t + 4$$

Simplify

The second derivative [src]

$$6$$

Simplify

The third derivative [src]

$$0$$

Simplify