Calculus Examples

$e^{2 x} (1 - 5 e^{3 x})$

Step 1

Apply the distributive property.

$e^{2 x} \cdot 1 + e^{2 x} (- 5 e^{3 x})$

Step 2

Simplify the expression.

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Step 2.1

Multiply $e^{2 x}$ by $1$ .

$e^{2 x} + e^{2 x} (- 5 e^{3 x})$

Step 2.2

Rewrite using the commutative property of multiplication.

$e^{2 x} - 5 e^{2 x} e^{3 x}$

Step 3

Multiply $e^{2 x}$ by $e^{3 x}$ by adding the exponents.

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Step 3.1

Move $e^{3 x}$ .

$e^{2 x} - 5 (e^{3 x} e^{2 x})$

Step 3.2

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

$e^{2 x} - 5 e^{3 x + 2 x}$

Step 3.3

Add $3 x$ and $2 x$ .

$e^{2 x} - 5 e^{5 x}$