What is the derivative of (0.09(5^x)/(x^3)) ?

The derivative of (0.09(5^x)/(x^3)) is (0.09*5^x(1.60943…x-3))/(x^4)

What is the first derivative of (0.09(5^x)/(x^3)) ?

The first derivative of (0.09(5^x)/(x^3)) is (0.09*5^x(1.60943…x-3))/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{0.09 ( 5 ^{x} )}{x ^{3}})

\frac{0.09 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{0.09 ( 5 ^{x} )}{x ^{3}})

Take the constant out:

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

= 0.09 \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}}

= 0.09 \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}

= 0.09 \cdot \frac{5 ^{x} ln ( 5 ) x ^{3} - 3 x ^{2} \cdot 5 ^{x}}{( x ^{3} ) ^{2}}

Simplify

0.09 \cdot \frac{5 ^{x} ln ( 5 ) x ^{3} - 3 x ^{2} \cdot 5 ^{x}}{( x ^{3} ) ^{2}} : \frac{0.09 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

= \frac{0.09 \cdot 5 ^{x} ( 1.60943 \dots x - 3 )}{x ^{4}}

\frac{d}{d x} (ln (\frac{3 x}{4}))

y^{^{'}} = \frac{x ( x ^{2} + 1 )}{4 y ^{3}}

\int \frac{3}{x ^{4}} + \frac{4}{x ^{2}} - \frac{6}{x ^{3}} d x

2 t y^{^{'}} + (4 + 12 t^{3} - 120 t^{2}) y = 0

y = (5 t - 1) (6 t - 3)^{- 1}

What is the derivative of (0.09(5^x)/(x^3)) ?
The derivative of (0.09(5^x)/(x^3)) is (0.09*5^x(1.60943…x-3))/(x^4)
What is the first derivative of (0.09(5^x)/(x^3)) ?
The first derivative of (0.09(5^x)/(x^3)) is (0.09*5^x(1.60943…x-3))/(x^4)