Derivative of sin(x)^x

Answer

\mathrm{sin}\left(x\right)^{x} \cdot \left(\frac{\mathrm{cos}\left(x\right) \cdot x}{\mathrm{sin}\left(x\right)}+\ln\left(\mathrm{sin}\left(x\right)\right)\right)

Derivative of sin(x)^x

Rule Used: Chain Rule
Steps: Identify a composite function in $\sin(x)$ ^x: 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: ( $\cos(x)$ * $\sin(x)^{-1}$ *x+ $\ln(\sin(x))$ )* $\sin(x)$ ^x

The derivative of sin(x)^x is (cos(x)*sin(x)^(-1)*x+ln(sin(x)))*sin(x)^x.

Instant step-by-step solution for sin(x)^x

Derivative TrigonometricIntermediate

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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/derivative-of-sinx-minus-to-minus-the-minus-x

How to find the derivative of sin(x)^x

To find the derivative of sin(x)^x, 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 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.

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