What is the derivative of f(x)=((e^{4x})/(x^6))^3 ?

The derivative of f(x)=((e^{4x})/(x^6))^3 is (6e^{12x}(2x-3))/(x^{19)}

What is the first derivative of f(x)=((e^{4x})/(x^6))^3 ?

The first derivative of f(x)=((e^{4x})/(x^6))^3 is (6e^{12x}(2x-3))/(x^{19)}

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derivative of

f (x) = (\frac{e ^{4 x}}{x ^{6}})^{3}

\frac{6 e ^{12 x} ( 2 x - 3 )}{x ^{19}}

Solution steps

\frac{d}{d x} ((\frac{e ^{4 x}}{x ^{6}})^{3})

Apply the chain rule:

3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{d}{d x} (\frac{e ^{4 x}}{x ^{6}})

= 3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{d}{d x} (\frac{e ^{4 x}}{x ^{6}})

\frac{d}{d x} (\frac{e ^{4 x}}{x ^{6}}) = \frac{2 e ^{4 x} ( 2 x - 3 )}{x ^{7}}

= 3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{2 e ^{4 x} ( 2 x - 3 )}{x ^{7}}

Simplify

3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{2 e ^{4 x} ( 2 x - 3 )}{x ^{7}} : \frac{6 e ^{12 x} ( 2 x - 3 )}{x ^{19}}

= \frac{6 e ^{12 x} ( 2 x - 3 )}{x ^{19}}

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What is the derivative of f(x)=((e^{4x})/(x^6))^3 ?
The derivative of f(x)=((e^{4x})/(x^6))^3 is (6e^{12x}(2x-3))/(x^{19)}
What is the first derivative of f(x)=((e^{4x})/(x^6))^3 ?
The first derivative of f(x)=((e^{4x})/(x^6))^3 is (6e^{12x}(2x-3))/(x^{19)}