What is the derivative of (0.3(9^x))/(x^3) ?

The derivative of (0.3(9^x))/(x^3) is (0.3*9^x(2.19722…x-3))/(x^4)

What is the first derivative of (0.3(9^x))/(x^3) ?

The first derivative of (0.3(9^x))/(x^3) is (0.3*9^x(2.19722…x-3))/(x^4)

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derivative of

\frac{0.3 ( 9 ^{x} )}{x ^{3}}

\frac{0.3 \cdot 9 ^{x} ( 2.19722 \dots x - 3 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{0.3 \cdot 9 ^{x}}{x ^{3}})

Take the constant out:

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

= 0.3 \frac{d}{d x} (\frac{9 ^{x}}{x ^{3}})

Apply the Quotient Rule:

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

= 0.3 \cdot \frac{\frac{d}{d x} ( 9 ^{x} ) x ^{3} - \frac{d}{d x} ( x ^{3} ) 9 ^{x}}{( x ^{3} ) ^{2}}

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

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

= 0.3 \cdot \frac{2 ln ( 3 ) \cdot 9 ^{x} x ^{3} - 3 x ^{2} \cdot 9 ^{x}}{( x ^{3} ) ^{2}}

Simplify

0.3 \cdot \frac{2 ln ( 3 ) \cdot 9 ^{x} x ^{3} - 3 x ^{2} \cdot 9 ^{x}}{( x ^{3} ) ^{2}} : \frac{0.3 \cdot 9 ^{x} ( 2.19722 \dots x - 3 )}{x ^{4}}

= \frac{0.3 \cdot 9 ^{x} ( 2.19722 \dots x - 3 )}{x ^{4}}

\int (cos (x) + \frac{1}{2} x) d x

tan (2 x)

g (t) = \frac{t - t}{t ^{\frac{1}{6}}}

\frac{d y}{d x} - y = \frac{e ^{x}}{y}

\frac{\partial}{\partial x} ((x^{2})^{- \frac{1}{2}})

What is the derivative of (0.3(9^x))/(x^3) ?
The derivative of (0.3(9^x))/(x^3) is (0.3*9^x(2.19722…x-3))/(x^4)
What is the first derivative of (0.3(9^x))/(x^3) ?
The first derivative of (0.3(9^x))/(x^3) is (0.3*9^x(2.19722…x-3))/(x^4)