Solved Examples on Derivative of 2x
Example 1: Find the derivative of 2x ·tan x.
Solution:
Let f(x) = 2x· tan x = u·v
By product rule,
f'(x) = u·v’ + v·u’
⇒ (2x) d/dx (tan x) + (tan x) d/dx (2x)
⇒ (2x)(sec2x) + (tan x) (2x·ln 2)
Therefore f'(x) = (2x)(sec2x) + (tan x) (2x·ln 2)
Example 2: Find the derivative of (2x)2.
Solution:
Let f(x) = (2x)2 = 22x
By chain rule,
f'(x) = 22x ln 2 d/dx[2x]
⇒ 2·22x·ln 2
⇒ 22x+1·ln 2
Therefore f'(x)= 22x+1·ln 2
Example 3: Find the derivative of 5x + 5x2
Solution:
Let f(x)=5x+5x2
f'(x)=5x·ln 5 + 5·2·x
⇒ 5x·ln 5 + 10·x
Therefore f'(x)= 5x·ln 5 + 10·x
Derivative of 2 to the x
Derivative of 2x is 2xln2. The Derivative of 2x refers to the process of finding change in 2x function to the independent variable. The method of finding the derivative for 2x functions is referred to as exponential differentiation.
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