What is the derivative of (0.3(5^x))/(x^3) ?

The derivative of (0.3(5^x))/(x^3) is (0.3*5^x(1.60943…x-3))/(x^4)

What is the first derivative of (0.3(5^x))/(x^3) ?

The first derivative of (0.3(5^x))/(x^3) is (0.3*5^x(1.60943…x-3))/(x^4)

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derivative of

\frac{0.3 ( 5 ^{x} )}{x ^{3}}

\frac{0.3 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{0.3 \cdot 5 ^{x}}{x ^{3}})

Take the constant out:

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

= 0.3 \frac{d}{d x} (\frac{5 ^{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} ( 5 ^{x} ) x ^{3} - \frac{d}{d x} ( x ^{3} ) 5 ^{x}}{( x ^{3} ) ^{2}}

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

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

= 0.3 \cdot \frac{5 ^{x} ln ( 5 ) x ^{3} - 3 x ^{2} \cdot 5 ^{x}}{( x ^{3} ) ^{2}}

Simplify

0.3 \cdot \frac{5 ^{x} ln ( 5 ) x ^{3} - 3 x ^{2} \cdot 5 ^{x}}{( x ^{3} ) ^{2}} : \frac{0.3 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

= \frac{0.3 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

cos (x^{2}), 0

x \to 1 lim (- 6)

x \to - π lim (cos (x + π) - 1)

\int \frac{1}{( 4 x ^{2} - 25 ) ^{2}} d x

x - 1, 2 x + 6, [- 2, 4]

What is the derivative of (0.3(5^x))/(x^3) ?
The derivative of (0.3(5^x))/(x^3) is (0.3*5^x(1.60943…x-3))/(x^4)
What is the first derivative of (0.3(5^x))/(x^3) ?
The first derivative of (0.3(5^x))/(x^3) is (0.3*5^x(1.60943…x-3))/(x^4)