Dangerous Differentiation

Calculus Level 2

Find out the differentiation of the function:- y = 10 0 x y=100^x With respect to x at x=1 correct upto two decimal places


The answer is 460.51.

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Aman Sharma by Aman Sharma , 25, India

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2 solutions

Hello and peace be upon you,

Taking ln on both sides,

ln y = x ln 100,

Differentiate on both sides with respect to x,

(1/y) dy / dx = ln 100 ,

dy / dx = y ln 100 = 100^x ln 100 ,

as x = 100,

dy / dx = 100 ln 100 = 460.52...

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Daniel Ferreira
Feb 22, 2015

y = 10 0 x f ( x ) = 10 0 x f ′ ( x ) = 10 0 x ⋅ ( ln ⁡ 100 ) ⋅ 1 f ′ ( x ) = 10 0 x ⋅ 4 , 6 f ′ ( 1 ) = 10 0 1 ⋅ 4 , 6 f ′ ( 1 ) = 460 y = 100^x \\\\ f(x) = 100^x \\\\ f'(x) = 100^x \cdot (\ln 100) \cdot 1 \\\\ f'(x) = 100^x \cdot 4,6 \\\\ f'(1) = 100^1 \cdot 4,6 \\\\ \boxed{f'(1) = 460}

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