Derivative of e^(6x)*cos(4x)

Answer

−4⋅3253681256⋅x⋅sin(4⋅x)1196962446⋅x+6⋅3253681256⋅x⋅cos(4⋅x)1196962446⋅x-\frac{4 \cdot 325368125^{6 \cdot x} \cdot \mathrm{sin}\left(4 \cdot x\right)}{119696244^{6 \cdot x}}+\frac{6 \cdot 325368125^{6 \cdot x} \cdot \mathrm{cos}\left(4 \cdot x\right)}{119696244^{6 \cdot x}}
-4*e^(6*x)*sin(4*x)+6*e^(6*x)*cos(4*x)

Derivative of e^(6x)*cos(4x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in e6⋅xe^{6 \cdot x}*cos⁡(4⋅x)\cos(4 \cdot x): use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
  2. Differentiate each factor and combine.
  3. Final answer: -4⋅e6⋅x4 \cdot e^{6 \cdot x}*sin⁡(4⋅x)\sin(4 \cdot x)+6⋅e6⋅x6 \cdot e^{6 \cdot x}*cos⁡(4⋅x)\cos(4 \cdot x)

The derivative of e^(6*x)*cos(4*x) is -4*e^(6*x)*sin(4*x)+6*e^(6*x)*cos(4*x).

Instant step-by-step solution for e^(6x)*cos(4x)

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Derivative of e^(6x)*cos(4x) = -4*e^(6*x)*sin(4*x)+6*e^(6*x)*cos(4*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-6xcos4x

How to find the derivative of e^(6x)*cos(4x)

To find the derivative of e^(6x)*cos(4x), 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^(6x)*cos(4x)?▼
The derivative of e^(6x)*cos(4x) is -4*e^(6*x)*sin(4*x)+6*e^(6*x)*cos(4*x).
How do you find the derivative of e^(6x)*cos(4x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -4*e^(6*x)*sin(4*x)+6*e^(6*x)*cos(4*x).
Why is the derivative of e^(6x)*cos(4x) equal to -4*e^(6*x)*sin(4*x)+6*e^(6*x)*cos(4*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(6x)*cos(4x) yields -4*e^(6*x)*sin(4*x)+6*e^(6*x)*cos(4*x). See the full step-by-step breakdown above.

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