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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 the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{x^{8\cos\left(x\right)}}\frac{d}{dx}\left(x^{8\cos\left(x\right)}\right)$
Learn how to solve problems step by step online. Find the derivative of ln(x^(8cos(x))). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative \frac{d}{dx}\left(x^{8\cos\left(x\right)}\right) results in 8\left(-\sin\left(x\right)\ln\left(x\right)+\frac{\cos\left(x\right)}{x}\right)x^{8\cos\left(x\right)}. Multiplying the fraction by 8\left(-\sin\left(x\right)\ln\left(x\right)+\frac{\cos\left(x\right)}{x}\right)x^{8\cos\left(x\right)}. Any expression multiplied by 1 is equal to itself.
