What is the derivative of y=((x^3))/(3^x) ?

The derivative of y=((x^3))/(3^x) is (x^2(3-ln(3)x))/(3^x)

What is the first derivative of y=((x^3))/(3^x) ?

The first derivative of y=((x^3))/(3^x) is (x^2(3-ln(3)x))/(3^x)

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derivative of

y = \frac{( x ^{3} )}{3 ^{x}}

\frac{x ^{2} ( 3 - ln ( 3 ) x )}{3 ^{x}}

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{3 ^{x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{3} ) 3 ^{x} - \frac{d}{d x} ( 3 ^{x} ) x ^{3}}{( 3 ^{x} ) ^{2}}

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

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

= \frac{3 x ^{2} \cdot 3 ^{x} - 3 ^{x} ln ( 3 ) x ^{3}}{( 3 ^{x} ) ^{2}}

Simplify

\frac{3 x ^{2} \cdot 3 ^{x} - 3 ^{x} ln ( 3 ) x ^{3}}{( 3 ^{x} ) ^{2}} : \frac{x ^{2} ( 3 - ln ( 3 ) x )}{3 ^{x}}

= \frac{x ^{2} ( 3 - ln ( 3 ) x )}{3 ^{x}}

What is the derivative of y=((x^3))/(3^x) ?
The derivative of y=((x^3))/(3^x) is (x^2(3-ln(3)x))/(3^x)
What is the first derivative of y=((x^3))/(3^x) ?
The first derivative of y=((x^3))/(3^x) is (x^2(3-ln(3)x))/(3^x)