# How do you find the derivative of #y=( (2x^3)*(e^(sinx))*(2^(cosx)) ) / (tanx-3^x)#?

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To find the derivative of the given function y=( (2x^3)*(e^(sinx))*(2^(cosx)) ) / (tanx-3^x), we can use the quotient rule. The quotient rule states that if we have a function in the form of f(x)/g(x), then the derivative is given by (g(x)*f'(x) - f(x)*g'(x)) / (g(x))^2.

Let's denote f(x) = (2x^3)*(e^(sinx))*(2^(cosx)) and g(x) = (tanx-3^x).

Now, we need to find the derivatives of f(x) and g(x) with respect to x:

f'(x) = d/dx (2x^3*e^(sinx)*2^(cosx)) g'(x) = d/dx (tanx - 3^x)

Using the product rule for f'(x) and the derivative of tanx and 3^x for g'(x), we can compute these derivatives.

After finding f'(x) and g'(x), we can substitute these values into the quotient rule formula and simplify to get the derivative of y with respect to x.

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