Calculus Examples

$\frac{d^{2} v}{d t^{2}}$ , $v = 2 t^{2} + 6 t + 15$

Step 1

Replace the variable $v$ with $2 t^{2} + 6 t + 15$ in the expression.

$\frac{d^{2} (2 t^{2} + 6 t + 15)}{d t^{2}}$

Step 2

Cancel the common factor of $d^{2}$ and $d$ .

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Step 2.1

Factor $d$ out of $d^{2} (2 t^{2} + 6 t + 15)$ .

$\frac{d (d (2 t^{2} + 6 t + 15))}{d t^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $d$ out of $d t^{2}$ .

$\frac{d (d (2 t^{2} + 6 t + 15))}{d (t^{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{d (d (2 t^{2} + 6 t + 15))}{d t^{2}}$

Step 2.2.3

Rewrite the expression.

$\frac{d (2 t^{2} + 6 t + 15)}{t^{2}}$