Question

Find the derivative of g(x)=\frac{5 e^{x}+9}{6 x^{3}+2 x^{5}} -45 x^{2}-15 x e^{x}-5 x^{3} e^{x}+25 x^{2} e^{x}+81+45 e^{x} g'(x)=

Answer 1

Answer and Step-by-step explanation:

The derivative of the function g(x) = (5e^x + 9)/(6x^3 + 2x^5) - 45x^2 - 15xe^x - 5x^3e^x + 25x^2e^x + 81 + 45e^x can be found using the quotient rule, the power rule, and the chain rule. The derivative is:

g'(x) = (5e^x(6x^3 + 2x^5) - (5e^x + 9)(18x^2 + 10x^4))/(6x^3 + 2x^5)^2 - 90x - 15e^x - 15xe^x - 15x^2e^x - 15x^3e^x + 50xe^x + 45e^x

Simplifying this expression, we get:

g'(x) = (-20e^(2x)x^4 - 10e^(2x)x^3 - 90e^(2)x - 90e^(2)x - 90e^(2)x + 50xe^(2)x + 45e^(2)x)/(6x^3 + 2x^5)^2 -90 x-15 e^{(2)x}-15 x e^{(2)x}-15 x^{(2)} e^{(2)x}-15 x^{(3)} e^{(2)x}+50 x e^{(2)x}+45 e^{(2)x}