Question

Find the derivative of y=e^-4x

Answer 1

The derivative of y = e^-4x is -4e^-4x.

Step-by-step explanation:

To find the derivative of y = e-4x, we can use the power rule for derivatives. The power rule states that if we have a function of the form y = axb, then the derivative is given by dy/dx = abxb-1. Applying this rule to the given function, we have dy/dx = -4e-4x. Therefore, the derivative of y = e-4x is -4e-4x.

Answer 2

`\displaystyle y' = -4e^(-4x)`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:
`\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)`

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
`\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

Step-by-step explanation:

Step 1: Define

Identify

`\displaystyle y = e^(-4x)`

Step 2: Differentiate

1. Exponential Differentiation [Derivative Rule - Chain Rule]:
   `\displaystyle y' = e^(-4x)(-4x)'`
2. Basic Power Rule [Derivative Property - Multiplied Constant]:
   `\displaystyle y' = -4e^(-4x)`

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation