What is the derivative of f(x)=(5^x)/(x^5) ?

The derivative of f(x)=(5^x)/(x^5) is (5^x(ln(5)x-5))/(x^6)

What is the first derivative of f(x)=(5^x)/(x^5) ?

The first derivative of f(x)=(5^x)/(x^5) is (5^x(ln(5)x-5))/(x^6)

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derivative of

f (x) = \frac{5 ^{x}}{x ^{5}}

\frac{5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{5 ^{x}}{x ^{5}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 ^{x} ) x ^{5} - \frac{d}{d x} ( x ^{5} ) 5 ^{x}}{( x ^{5} ) ^{2}}

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{5 ^{x} ln ( 5 ) x ^{5} - 5 x ^{4} \cdot 5 ^{x}}{( x ^{5} ) ^{2}}

Simplify

\frac{5 ^{x} ln ( 5 ) x ^{5} - 5 x ^{4} \cdot 5 ^{x}}{( x ^{5} ) ^{2}} : \frac{5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

= \frac{5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

\frac{d}{d x} (sin (\frac{π x}{7}))

\int 2 x - 1 d x

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What is the derivative of f(x)=(5^x)/(x^5) ?
The derivative of f(x)=(5^x)/(x^5) is (5^x(ln(5)x-5))/(x^6)
What is the first derivative of f(x)=(5^x)/(x^5) ?
The first derivative of f(x)=(5^x)/(x^5) is (5^x(ln(5)x-5))/(x^6)