Thursday, December 20, 2012

`y = 5^(-4x)` Find the derivative of the function

`y=5^(-4x)`


The derivative formula of an exponential function is:


`d/(dx) (a^u) = ln(a) * a^u * (du)/(dx)`


Applying this formula, the derivative of the function is:


`(dy)/(dx) = d/(dx)(5^(-4x))`


`(dy)/(dx) = ln(5) * 5^(-4x) * d/(dx)(-4x)`


`(dy)/(dx) = ln(5) * 5^(-4x) * (-4)`


`(dy)/(dx) = -4 ln(5) * 5^(-4x)`



Therefore, `(dy)/(dx) = -4ln(5) * 5^(-4x)` .

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