Find the derivative of $x^x\frac{x^9\tan\left(x\right)}{\cos\left(x\right)\sin\left(x\right)}$

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$\frac{d}{dx}\left(\frac{x^{\left(9+x\right)}\sec\left(x\right)}{\cos\left(x\right)}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of x^x(x^9tan(x))/(cos(x)sin(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}}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^{\left(9+x\right)} and g=\sec\left(x\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).