Final answer to the problem
Step-by-step Solution
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- Choose an option
- 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 the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^{\ln\left(x\right)}$ and $g=\sec\left(x\right)^{3x}$
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$\frac{d}{dx}\left(x^{\ln\left(x\right)}\right)\sec\left(x\right)^{3x}+x^{\ln\left(x\right)}\frac{d}{dx}\left(\sec\left(x\right)^{3x}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of x^ln(x)sec(x)^(3x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^{\ln\left(x\right)} and g=\sec\left(x\right)^{3x}. The derivative \frac{d}{dx}\left(x^{\ln\left(x\right)}\right) results in 2x^{\left(\ln\left(x\right)-1\right)}\ln\left(x\right). The derivative \frac{d}{dx}\left(\sec\left(x\right)^{3x}\right) results in 3\left(\ln\left(\sec\left(x\right)\right)+x\tan\left(x\right)\right)\sec\left(x\right)^{3x}.
