Question

Who can resolve this derivative:
f (x) = x / x*4 -5

Answer 1

Explanation:

Functions used:

`\displaystyle\\\boxed {((u)/(v))'=(u'v-v'u)/(v^2) }\ \ \ \ \ \boxed {(u+v)'=u'+v'}\ \ \ \ \ \boxed {(x^n)'=n*x^(n-1)}`

`\displaystyle\\f(x)=(x)/(x^4-5) \\\\f'(x)=((x)/(x^4-5))'\\ f'(x)=(x'(x^4-5)-(x^4-5)'x)/((x^4-5)^2) \\\\f'(x)=(1(x^4-5)-((x^4)'-5')x)/((x^4-5)^2)\\\\f'(x)=(x^4-5-(4x^3-0)x)/((x^4-5)^2) \\\\f'(x)=(x^4-5-(4x^3)x)/((x^4-5)^2)\\\\f'(x)=(x^4-5-4x^4)/((x^4-5)^2) \\\\f'({x)=(-3x^4-5)/((x^4-5)^2) \\\\`

`\displaystyle\\f'(x)=(-(3x^4+5))/((x^4-5)^2) \\\\f'(x)=-(3x^4+5)/((x^4-5)^2)`