Question

y= 36^log base(6) x then dy/dx ​

Answer 1

Answer:

as e^logx

=x

so here 36^log6x

=36.6x

so dy/dx= 216

Answer 2

Answer: Value of dy/dx is 2x

Step-by-step explanation:

$y = 36^{log_6x}$

⇒ $y = (6^{2} )^{log_6x}$

Using the property $(a^{m})^{n} = a^{mn}$

⇒ $y = 6^{2log_6x}$    

⇒ $y = 6^{log_6x^{2} }$

Using the property  $x^{log_ba} = a^{log_bx}$

⇒ $y = (x^{2}) ^{log_66}$

⇒ $y = x^{2}$

Taking derivative of both sides with respect to x,

$\frac{dy}{dx} = 2x$

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