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

Question

f(x)= 3/x³+6/√x +7

f’(x)= ?

Answer 1

use either the derivative of a fraction or do it as an exponent

as a fraction, the derivative is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the denominator squared. That's a little tedious, but it's a check on whether you got it right, when you do it the other way with just an exponent.

f = 3/x^3 + 6/sqrx + 7

f' = -3(3x^2/x^6 - 6(1/2)sqr^-1/2/x

=-9/x^4 -3x^-3/2 = -9/x^4 - 3/xsqrx

or just keep them as negative exponents

f=3x^-3 + 6x^-1/2 + 7

f'= -9x^-4 -3x^-3/2

= -9/x^4 - 3/xsqrx

(x^3/2 = xsqrx or = x(x^1/2) )

Answer 2

Power rule: when f(x) = a xⁿ, f'(x) = an x^n-1. Rewrite the given expression as f(x) = 3 x^-3 + 6 x^-1/2 + 7, then f'(x) = -9 x^-4 - 3 x^-3/2 + 0.