Differentiation: Extending the rule

Question 1

Differentiate y =1/x

Answer 1

First write the expression as a power of x
y = 1/x = x^−1
Subtracting 1 from −1 gives −2
dy/dx = −1x^−2 = -1/x^2

Question 2

Differentiate y=(3−2x−x2) rootx

Answer 2

Question 3

Answer 3

Question 4

Answer 4

y=(x^2 −3)/x^3
=1/x−3/x^3
=x^−1 −3x^−3
dy =−x^−2 +9x^−4 = -1/x^2 + 9/x^4