Find the derivative of the function by using the rules of differentiation.

Question

f(x)= 9/x³-3/x²-1/x+150

f’(x)= ?

Answer 1

f(x) = 9/x^3 -3/x^2 -1/x + 150

the derivative of a fraction is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the denominator squared:

f'(x) =-9(3)x^2/x^6 +3(2)x/x^4 + 1/x^2

f'(x) =- 27/x^4 + 6/x^3 + 1/x^2

Answer 2

It is easier to differentiate to rewrite the function as:

f(x) = 9x^-3-3x^-2-x^-1+150

Then just use the differentiaion rules: dxⁿ/dx = nx^n-1 and d af(x)/dx = af'(x)

f'(x) = -27x^-4+6x^-3+x^-2 = -27/x⁴+6/x³+1/x²