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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
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$\frac{d}{dx}\left(\cos\left(x\right)^{\log \left(x\right)}\right)+\frac{d}{dx}\left(\log \left(x\right)^x\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(cos(x)^log(x)+log(x)^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 \frac{d}{dx}\left(\cos\left(x\right)^{\log \left(x\right)}\right) results in \left(\frac{\ln\left(\cos\left(x\right)\right)}{\ln\left(10\right)x}+\frac{-\log \left(x\right)\sin\left(x\right)}{\cos\left(x\right)}\right)\cos\left(x\right)^{\log \left(x\right)}. The derivative \frac{d}{dx}\left(\log \left(x\right)^x\right) results in \left(\ln\left(\log \left(x\right)\right)+\frac{1}{\ln\left(10\right)\log \left(x\right)}\right)\log \left(x\right)^x. Simplify the derivative.
