If y = 4x² + 2x² +6/x+3, then find dy/dx =?
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dy
=
dx
d
[4x
4
+2x
3
+
x
5
+9]
(Differentiating both sides w.r.t. x)
=
dx
d
[4x
4
]+
dx
d
[2x
3
]+
dx
d
[
x
5
]+
dx
d(9)
(Using the property of linearity)
=
dx
d
[4x
4
]+
dx
d
[2x
3
]+
dx
d
[
x
5
]
(As differentiation of constant =0,
dx
d9
=0)
=4
dx
d
,[x]
4
+2
dx
d
[x
3
]+5
dx
d
[x
−1
] (Separating constant coefficients)
=4×4x
3
+2×3x
2
+5(−1)x
−2
=16x
3
+6x
2
−
x
2
5
.
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