What is the derivative of (3(9^x)/(x^5)) ?

The derivative of (3(9^x)/(x^5)) is (3^{2x+1}(2ln(3)x-5))/(x^6)

What is the first derivative of (3(9^x)/(x^5)) ?

The first derivative of (3(9^x)/(x^5)) is (3^{2x+1}(2ln(3)x-5))/(x^6)

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\frac{d}{d x} (\frac{3 ( 9 ^{x} )}{x ^{5}})

\frac{3 ^{2 x + 1} ( 2 ln ( 3 ) x - 5 )}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{3 ( 9 ^{x} )}{x ^{5}})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{9 ^{x}}{x ^{5}})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d}{d x} ( 9 ^{x} ) x ^{5} - \frac{d}{d x} ( x ^{5} ) 9 ^{x}}{( x ^{5} ) ^{2}}

\frac{d}{d x} (9^{x}) = 2 ln (3) \cdot 9^{x}

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

= 3 \cdot \frac{2 ln ( 3 ) \cdot 9 ^{x} x ^{5} - 5 x ^{4} \cdot 9 ^{x}}{( x ^{5} ) ^{2}}

Simplify

3 \cdot \frac{2 ln ( 3 ) \cdot 9 ^{x} x ^{5} - 5 x ^{4} \cdot 9 ^{x}}{( x ^{5} ) ^{2}} : \frac{3 ^{2 x + 1} ( 2 ln ( 3 ) x - 5 )}{x ^{6}}

= \frac{3 ^{2 x + 1} ( 2 ln ( 3 ) x - 5 )}{x ^{6}}

\int \frac{1}{x ^{5}} sin (\frac{1}{x ^{4}}) d x

y^{^{'}} - 4 y^{2} = 2 t y^{2}

2 x^{3} y^{^{'}} = y (2 x^{2} - y^{2})

f (x) = 12 (x - \frac{1}{x})^{2}, at x = 2

\int \frac{( e ^{x} + e ^{- x} )}{2} d x

What is the derivative of (3(9^x)/(x^5)) ?
The derivative of (3(9^x)/(x^5)) is (3^{2x+1}(2ln(3)x-5))/(x^6)
What is the first derivative of (3(9^x)/(x^5)) ?
The first derivative of (3(9^x)/(x^5)) is (3^{2x+1}(2ln(3)x-5))/(x^6)