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

The derivative of (3^x/(x^3)) is (3^x(ln(3)x-3))/(x^4)

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

The first derivative of (3^x/(x^3)) is (3^x(ln(3)x-3))/(x^4)

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

\frac{3 ^{x} ( ln ( 3 ) x - 3 )}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{3 ^{x} ln ( 3 ) x ^{3} - 3 x ^{2} \cdot 3 ^{x}}{( x ^{3} ) ^{2}} : \frac{3 ^{x} ( ln ( 3 ) x - 3 )}{x ^{4}}

= \frac{3 ^{x} ( ln ( 3 ) x - 3 )}{x ^{4}}

\int_{0}^{1} (- x + 2) - (x^{2} - 1) d x

\int x^{3} e^{x} d x

(x^{3} + y^{3}) d x + 3 x y^{2} d y = 0

\frac{d}{d x} ((8 x + 7)^{2})

\int \frac{1}{cos ( 3 x )} d x

What is the derivative of (3^x/(x^3)) ?
The derivative of (3^x/(x^3)) is (3^x(ln(3)x-3))/(x^4)
What is the first derivative of (3^x/(x^3)) ?
The first derivative of (3^x/(x^3)) is (3^x(ln(3)x-3))/(x^4)