Find the derivative of 5^3x-1 using first principle
Answers
Answered by
1
Answer:
Step-by-step explanation:
Let f(x)=(5x^3+3x−1)(x−1)
Thus using product rule of differentiation,
f (x)=(5x^3+3x−1)
dxd
(x−1)+(x−1)
dx
d
(5x
3
+3x−1)
=(5x
3
+3x−1)(1)+(x−1)(5.3x
2
+3−0)
=(5x
3
+3x−1)+(x−1)(15x
2
+3)
=5x
3
+3x−1+15x
3
+3x−15x
2
−3
=20x
3
−15x
2
+6x−4
Answered by
8
Answer:
The first principle says:
f’(x) = lim h→0 [ (f(x+h) - f(x)) / h ]
So let’s look at it for the given function f(x) = 3x + 1
f(x+h) = 3(x+h) + 1
f(x) = 3x + 1
f(x+h) - f(x) = 3(x+h) + 1 - (3x + 1) = 3x + 3h + 1 - 3x - 1 = 3h
f’(x) = lim h→0 [ 3h/h ] = lim h→0 [ 3 ] = 3
Similar questions