Derivada de sin(x)^x
Answer
(cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x
Derivative of sin(x)^x
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in ^x: use the chain rule = 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: (**x+)*^x
La derivada de sin(x)^x es (cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x.
Solución paso a paso instantánea para sin(x)^x
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Derivative of sin(x)^x = (cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-sinx-minus-to-minus-the-minus-x
Cómo encontrar la derivada de sin(x)^x
Para encontrar la derivada de sin(x)^x, usamos reglas de diferenciación estándar. Nuestra calculadora con IA desglosa los pasos y explica la lógica.
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Frequently Asked Questions
What is the derivative of sin(x)^x?▼
The derivative of sin(x)^x is (cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x.
How do you find the derivative of sin(x)^x?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is (cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x.
Why is the derivative of sin(x)^x equal to (cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x?▼
Because differentiation measures how a function changes — applying the rules to sin(x)^x yields (cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x. See the full step-by-step breakdown above.