Find the derivative

Question

[(x²+2x-3)÷(x³-7)] +x⁴

Answer 1

First, use the quotient rule.

 

derivative [f(x)/g(x)] = [derivative of f(x)*g(x) - (f(x)*derivative of g(x))]/g²(x) ,

 

where  f(x) = x²+2x-3   and   g(x) = x³-7

 

Second, use the power rule to find the derivative of x⁴. 

 

derivative of x⁴ = 4x^4-1 = 4x³.

 

Now add the results of the first and second step.