Derivative of e^(4x+5)

Answer

4 \cdot 119696244^{-4 \cdot x-5} \cdot 325368125^{4 \cdot x+5}

Derivative of e^(4x+5)

Rule Used: Chain Rule
Steps: Identify a composite function in $e^{4 \cdot x+5}$ : use the chain rule $\frac{d}{dx} f(g(x))$ = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
Differentiate the outer function, then multiply by the inner derivative.
Final answer: 4*119696244^(- $4 \cdot x$ -5)*325368125^( $4 \cdot x$ +5)

The derivative of e^(4*x+5) is 4*119696244^(-4*x-5)*325368125^(4*x+5).

Instant step-by-step solution for e^(4x+5)

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Derivative of e^(4x+5) = 4*119696244^(-4*x-5)*325368125^(4*x+5) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-4x-minus-plus-minus-5

How to find the derivative of e^(4x+5)

To find the derivative of e^(4x+5), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

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Frequently Asked Questions

What is the derivative of e^(4x+5)?▼

The derivative of e^(4x+5) is 4*119696244^(-4*x-5)*325368125^(4*x+5).

How do you find the derivative of e^(4x+5)?▼

Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 4*119696244^(-4*x-5)*325368125^(4*x+5).

Why is the derivative of e^(4x+5) equal to 4*119696244^(-4*x-5)*325368125^(4*x+5)?▼

Because differentiation measures how a function changes — applying the rules to e^(4x+5) yields 4*119696244^(-4*x-5)*325368125^(4*x+5). See the full step-by-step breakdown above.

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