What is the derivative of (7^x)/(x^3) ?

The derivative of (7^x)/(x^3) is (7^x(ln(7)x-3))/(x^4)

What is the first derivative of (7^x)/(x^3) ?

The first derivative of (7^x)/(x^3) is (7^x(ln(7)x-3))/(x^4)

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derivative of

\frac{7 ^{x}}{x ^{3}}

\frac{7 ^{x} ( ln ( 7 ) x - 3 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{7 ^{x}}{x ^{3}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

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

= \frac{7 ^{x} ln ( 7 ) x ^{3} - 3 x ^{2} \cdot 7 ^{x}}{( x ^{3} ) ^{2}}

Simplify

\frac{7 ^{x} ln ( 7 ) x ^{3} - 3 x ^{2} \cdot 7 ^{x}}{( x ^{3} ) ^{2}} : \frac{7 ^{x} ( ln ( 7 ) x - 3 )}{x ^{4}}

= \frac{7 ^{x} ( ln ( 7 ) x - 3 )}{x ^{4}}

What is the derivative of (7^x)/(x^3) ?
The derivative of (7^x)/(x^3) is (7^x(ln(7)x-3))/(x^4)
What is the first derivative of (7^x)/(x^3) ?
The first derivative of (7^x)/(x^3) is (7^x(ln(7)x-3))/(x^4)