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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable
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$\frac{d}{dx}\left(\sin\left(x\right)^y\right)=\frac{d}{dx}\left(y^x\right)$
Learn how to solve problems step by step online. Find the implicit derivative d/dx(sin(x)^y=y^x). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative \frac{d}{dx}\left(\sin\left(x\right)^y\right) results in \frac{\sin\left(x\right)^{\left(2y-1\right)}\cos\left(x\right)}{1-\ln\left(\sin\left(x\right)\right)\sin\left(x\right)^y}. The derivative \frac{d}{dx}\left(y^x\right) results in \frac{y^x\ln\left(y^x\right)}{1-x}. Simplify the derivative.