Question

Find dervatives of the following functions:
(i) `y=2x^(3)` , (ii) `y=4/x` , (iii) `y=3e^(x)` , (iv) `y=6 ln x` , (v) `y=5 sin x`

Answer 1

(i) `y=2x^(3)rArr (dy)/(dx)=2[3x^(3-1)]=6x^(2)` (ii) `y=4/x=4x^(-1)rArr (dy)/(dx)=4[(-1)x^(-1-1)]=-4/x^(2)`
(iii) `y=3e^(x)rArr (dy)/(dx)=3e^(x)` (iv) `y=6 ln xrArr (dy)/(dx)=6(1/x)=6/x`
(v) `y=5 sin xrArr (dy)/(dx)=5 (cos x)=5 cos x`