Final answer to the problem
Step-by-step Solution
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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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The derivative of a sum of two or more functions is the sum of the derivatives of each function
Learn how to solve sum rule of differentiation problems step by step online.
$\frac{d}{dx}\left(x^xy\right)+\frac{d}{dx}\left(\sin\left(x\right)^{\ln\left(x\right)}\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(x^xy+sin(x)^ln(x)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative \frac{d}{dx}\left(x^x\right) results in \left(\ln\left(x\right)+1\right)x^x. The derivative \frac{d}{dx}\left(\sin\left(x\right)^{\ln\left(x\right)}\right) results in \left(\frac{\ln\left(\sin\left(x\right)\right)}{x}+\frac{\ln\left(x\right)\cos\left(x\right)}{\sin\left(x\right)}\right)\sin\left(x\right)^{\ln\left(x\right)}.
