What is the derivative of (9(5^x)/(x^5)) ?

The derivative of (9(5^x)/(x^5)) is (9*5^x(ln(5)x-5))/(x^6)

What is the first derivative of (9(5^x)/(x^5)) ?

The first derivative of (9(5^x)/(x^5)) is (9*5^x(ln(5)x-5))/(x^6)

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\frac{d}{d x} (\frac{9 ( 5 ^{x} )}{x ^{5}})

\frac{9 \cdot 5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{9 ( 5 ^{x} )}{x ^{5}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \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}}

= 9 \cdot \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}

= 9 \cdot \frac{5 ^{x} ln ( 5 ) x ^{5} - 5 x ^{4} \cdot 5 ^{x}}{( x ^{5} ) ^{2}}

Simplify

9 \cdot \frac{5 ^{x} ln ( 5 ) x ^{5} - 5 x ^{4} \cdot 5 ^{x}}{( x ^{5} ) ^{2}} : \frac{9 \cdot 5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

= \frac{9 \cdot 5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

y^{^{''}} + 2 y^{^{'}} + 17 y = 0

\frac{d}{d x} (\frac{1}{x ^{2} + 9})

\int \frac{5 x ^{2}}{x ^{2} + 7} d x

\int sin^{3} (a x) d x

sin (x), sin (2 x), [0, \frac{π}{3}]

What is the derivative of (9(5^x)/(x^5)) ?
The derivative of (9(5^x)/(x^5)) is (9*5^x(ln(5)x-5))/(x^6)
What is the first derivative of (9(5^x)/(x^5)) ?
The first derivative of (9(5^x)/(x^5)) is (9*5^x(ln(5)x-5))/(x^6)