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

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

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

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

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derivative of

f (x) = \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}}

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

\int_{1}^{3} \frac{1}{1 + x ^{2}} d x

arctan (3 x^{2} - 1)

7 y^{^{''}} + y^{^{'}} = 0

n = 1 \sum \infty \frac{9}{n ^{2} + 1}

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