Calculus Examples

$(5 e^{4 x + 2}) \cdot (- 3 e^{2 x - 7})$

Step 1

Rewrite using the commutative property of multiplication.

$5 \cdot - 3 e^{4 x + 2} e^{2 x - 7}$

Step 2

Multiply $e^{4 x + 2}$ by $e^{2 x - 7}$ by adding the exponents.

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Step 2.1

Move $e^{2 x - 7}$ .

$5 \cdot - 3 (e^{2 x - 7} e^{4 x + 2})$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 \cdot - 3 e^{2 x - 7 + 4 x + 2}$

Step 2.3

Add $2 x$ and $4 x$ .

$5 \cdot - 3 e^{6 x - 7 + 2}$

Step 2.4

Add $- 7$ and $2$ .

$5 \cdot - 3 e^{6 x - 5}$

Step 3

Multiply $5$ by $- 3$ .

$- 15 e^{6 x - 5}$