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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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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\frac{x^6\sec\left(x\right)}{e^x}\right)$
Learn how to solve problems step by step online. Find the derivative d/dx((x^6tan(x))/(e^xsin(x))). Simplify the derivative by applying the properties of logarithms. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify \left(e^x\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals x and n equals 2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^6 and g=\sec\left(x\right).