(1) Find the derivatives of the following w.r.t.x.
by using method of first principle.
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Given:
The functions.
To find:
Find the derivatives w.r.t.x. by using method of first principle.
Solution:
From the given information, we have the data as follows.
(a) x² + 3x - 1
= d/dx (x² + 3x - 1)
= 2x + 3
(b) sin (3x)
= d/dx [sin (3x)]
= 3 cos 3x
(c) e^{2x + 1}
= d/dx [e^{2x + 1}]
= 2 e^{2x + 1}
(d) 3^x
= d/dx (3^x)
= 3^x ln 3
(e) log (2x + 5)
= d/dx [log (2x + 5)]
= 2/(2x + 5)
(f) tan (2x + 3)
= d/dx [tan (2x + 3)]
= 2 sec^2 (2x + 3)
(g) sec (5x - 2)
= d/dx [sec (5x - 2)]
= 5 sec (5x - 2) tan (5x - 2)
(h) x√x
= d/dx [x√x]
= 3/2 √x
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