find the derivatives of the following functions from the first principles x^+4
Answers
Answered by
2
Step-by-step explanation:
According to first principle:
f
′
(x)=
h→0
lim
h
f(x+h)−f(x)
Here, f(x)=x
4
+4
(x
3
)
′
=
h→0
lim
h
(x+h)
4
+4−x
4
−4
=
h→0
lim
h
x
4
+4x
3
h+6x
2
h
2
+4xh
3
+h
4
−x
4
=
h→0
lim
h
4x
3
h+6x
2
h
2
+4xh
3
+h
4
=
h→0
lim
4x
3
+6x
2
h+4xh
2
+h
3
=
4x
3
Answered by
0
Answer:
According to first principle:
f
′
(x)=
h→0
lim
h
f(x+h)−f(x)
Here, f(x)=x
4
+4
(x
3
)
′
=
h→0
lim
h
(x+h)
4
+4−x
4
−4
=
h→0
lim
h
x
4
+4x
3
h+6x
2
h
2
+4xh
3
+h
4
−x
4
=
h→0
lim
h
4x
3
h+6x
2
h
2
+4xh
3
+h
4
=
h→0
lim
4x
3
+6x
2
h+4xh
2
+h
3
=
4x
3
Step-by-step explanation:
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